BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Salma Kuhlmann (University of Konstanz)
DTSTART;VALUE=DATE-TIME:20210113T134500Z
DTEND;VALUE=DATE-TIME:20210113T150000Z
DTSTAMP;VALUE=DATE-TIME:20230208T070133Z
UID:ModelsandSets/1
DESCRIPTION:Title: Strongly NIP almost real closed fields\nby Salma Kuhlmann (Unive
rsity of Konstanz) as part of Leeds Models and Sets\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ModelsandSets/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rehana Patel (African Institute for Mathematical Sciences Senegal)
DTSTART;VALUE=DATE-TIME:20210120T134500Z
DTEND;VALUE=DATE-TIME:20210120T150000Z
DTSTAMP;VALUE=DATE-TIME:20230208T070133Z
UID:ModelsandSets/2
DESCRIPTION:Title: Combining logic and probability in the presence of symmetry\nby
Rehana Patel (African Institute for Mathematical Sciences Senegal) as part
of Leeds Models and Sets\n\n\nAbstract\nAmong the many approaches to comb
ining logic and probability\, an important one has been to assign probabil
ities to formulas of a classical logic\, instantiated from some fixed doma
in\, in a manner that respects logical structure. A natural additional con
dition is to require that the distribution satisfy the symmetry property k
nown as exchangeability. In this talk I will trace some of the history of
this line of investigation\, viewing exchangeability from a logical perspe
ctive. I will then report on the current status of a joint programme of Ac
kerman\, Freer and myself on countable exchangeable structures\, rounding
out a story that has its beginnings in Leeds in 2011.\n
LOCATION:https://researchseminars.org/talk/ModelsandSets/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tin Lok Wong (National University of Singapore)
DTSTART;VALUE=DATE-TIME:20210127T114500Z
DTEND;VALUE=DATE-TIME:20210127T130000Z
DTSTAMP;VALUE=DATE-TIME:20230208T070133Z
UID:ModelsandSets/3
DESCRIPTION:Title: Arithmetic under negated induction\nby Tin Lok Wong (National Un
iversity of Singapore) as part of Leeds Models and Sets\n\n\nAbstract\nAri
thmetic generally does not admit any non-trivial quantifier elimination. I
will talk about one exception\, where the negation of an induction axiom
is included in the theory. Here the Weak Koenig Lemma from reverse mathema
tics arises as a model completion.\nThis work is joint with Marta Fiori-Ca
rones\, Leszek Aleksander Kolodziejczyk and Keita Yokoyama.\n
LOCATION:https://researchseminars.org/talk/ModelsandSets/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lynn Scow (California State University\, San Bernardino)
DTSTART;VALUE=DATE-TIME:20210203T144500Z
DTEND;VALUE=DATE-TIME:20210203T160000Z
DTSTAMP;VALUE=DATE-TIME:20230208T070133Z
UID:ModelsandSets/4
DESCRIPTION:Title: Semi-retractions and preservation of the Ramsey property\nby Lyn
n Scow (California State University\, San Bernardino) as part of Leeds Mod
els and Sets\n\n\nAbstract\nFor structures $A$ and $B$ in possibly differe
nt languages we define what it means for $A$ to be a semi-retraction of $B
$. An injection $f:A \\rightarrow B$ is quantifier-free type respecting if
tuples from $A$ that share the same quantifier-free type in $A$ are mappe
d by $f$ to tuples in $B$ that share the same quantifier-free type in $B$.
We say that $A$ is a semi-retraction of $B$ if there are quantifier-free
type respecting injections $g: A \\rightarrow B$ and $f: B \\rightarrow A$
such that $f \\circ g : A \\rightarrow A$ is an embedding.\nWe will talk
about examples of semi-retractions and give conditions for when the Ramsey
property for (the age of) $B$ is inherited by a semi-retraction $A$ of $B
$.\n
LOCATION:https://researchseminars.org/talk/ModelsandSets/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adrian Mathias (Université de la Réunion)
DTSTART;VALUE=DATE-TIME:20210210T134500Z
DTEND;VALUE=DATE-TIME:20210210T150000Z
DTSTAMP;VALUE=DATE-TIME:20230208T070133Z
UID:ModelsandSets/5
DESCRIPTION:Title: Power-admissible sets and ill-founded omega-models\nby Adrian Ma
thias (Université de la Réunion) as part of Leeds Models and Sets\n\n\nA
bstract\nAbstract: In the 1960s admissible sets were introduced which are
transitive sets modelling principles of $\\Sigma_1$ set-recursion.\n\nIn 1
971 Harvey Friedman introduced power-admissible sets\, which are transitiv
e sets modelling principles of $\\Sigma_1^P$\, roughly $\\Sigma_1$ recursi
on in the power-set function.\n\nSeveral decades later I initiated the stu
dy of provident sets\, which are transitive sets modelling principles of r
udimentary recursion. Over the last fifty-odd years several workers have f
ound that ill-founded omega-models\, the axiom of constructibility and tec
hniques from proof theory bring unexpected insights into the structure of
these models of set-recursion.\n\nIn this talk I shall review these result
s and the methods of proof.\n
LOCATION:https://researchseminars.org/talk/ModelsandSets/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erin Carmody (Fordham College)
DTSTART;VALUE=DATE-TIME:20210217T164500Z
DTEND;VALUE=DATE-TIME:20210217T180000Z
DTSTAMP;VALUE=DATE-TIME:20230208T070133Z
UID:ModelsandSets/6
DESCRIPTION:Title: The relationships between measurable and strongly compact cardinals.
(Part 1)\nby Erin Carmody (Fordham College) as part of Leeds Models an
d Sets\n\n\nAbstract\nThis talk is about the ongoing investigation of the
relationships between measurable and strongly compact cardinals. I will p
resent some of the history of the theorems in this theme\, including Magid
or's identity crisis\, and give new results. The theorems presented are i
n particular about the relationships between strongly compact cardinals an
d measurable cardinals of different Mitchell orders. One of the main theor
ems is that there is a universe where $\\kappa_1$ and $\\kappa_2$ are the
first and second strongly compact cardinals\, respectively\, and where $\\
kappa_1$ is least with Mitchell order 1\, and $\\kappa_2$ is the least wit
h Mitchell order 2. Another main theorem is that there is a universe wher
e $\\kappa_1$ and $\\kappa_2$ are the first and second strongly compact ca
rdinals\, respectively\, with $\\kappa_1$ the least measurable cardinal su
ch that $o(\\kappa_1) = 2$ and $\\kappa_2$ the least measurable cardinal a
bove $\\kappa_1$. This is a joint work in progress with Victoria Gitman a
nd Arthur Apter.\n
LOCATION:https://researchseminars.org/talk/ModelsandSets/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erin Carmody (Fordham College)
DTSTART;VALUE=DATE-TIME:20210224T164500Z
DTEND;VALUE=DATE-TIME:20210224T180000Z
DTSTAMP;VALUE=DATE-TIME:20230208T070133Z
UID:ModelsandSets/7
DESCRIPTION:Title: The relationships between measurable and strongly compact cardinals.
(Part 2)\nby Erin Carmody (Fordham College) as part of Leeds Models an
d Sets\n\n\nAbstract\nThis talk is about the ongoing investigation of the
relationships between measurable and strongly compact cardinals. I will p
resent some of the history of the theorems in this theme\, including Magid
or's identity crisis\, and give new results. The theorems presented are i
n particular about the relationships between strongly compact cardinals an
d measurable cardinals of different Mitchell orders. One of the main theor
ems is that there is a universe where $\\kappa_1$ and $\\kappa_2$ are the
first and second strongly compact cardinals\, respectively\, and where $\\
kappa_1$ is least with Mitchell order 1\, and $\\kappa_2$ is the least wit
h Mitchell order 2. Another main theorem is that there is a universe wher
e $\\kappa_1$ and $\\kappa_2$ are the first and second strongly compact ca
rdinals\, respectively\, with $\\kappa_1$ the least measurable cardinal su
ch that $o(\\kappa_1) = 2$ and $\\kappa_2$ the least measurable cardinal a
bove $\\kappa_1$. This is a joint work in progress with Victoria Gitman a
nd Arthur Apter.\n
LOCATION:https://researchseminars.org/talk/ModelsandSets/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dana Bartošová (University of Florida)
DTSTART;VALUE=DATE-TIME:20210310T134500Z
DTEND;VALUE=DATE-TIME:20210310T150000Z
DTSTAMP;VALUE=DATE-TIME:20230208T070133Z
UID:ModelsandSets/8
DESCRIPTION:Title: Universal minimal flows of group extensions\nby Dana Bartošová
(University of Florida) as part of Leeds Models and Sets\n\n\nAbstract\nM
inimal flows of a topological group G are often described as the building
blocks of dynamical systems with the acting group G. The universal minimal
flow is the most complicated one\, in the sense that it is minimal and ad
mits a homomorphism onto any minimal flow. We will study how group extensi
ons interact with universal minimal flows\, in particular extensions of an
d by a compact group.\n
LOCATION:https://researchseminars.org/talk/ModelsandSets/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sonia Navarro Flores (Universidad Nacional Autónoma de México)
DTSTART;VALUE=DATE-TIME:20210317T144500Z
DTEND;VALUE=DATE-TIME:20210317T160000Z
DTSTAMP;VALUE=DATE-TIME:20230208T070133Z
UID:ModelsandSets/9
DESCRIPTION:Title: Ramsey spaces and Borel ideals\nby Sonia Navarro Flores (Univers
idad Nacional Autónoma de México) as part of Leeds Models and Sets\n\n\n
Abstract\nIt is known that the Ellentuck space\, which is forcing equivale
nt to the Boolean algebra P(\\omega)/Fin forces a selective ultrafilter. T
he Ellentuck space is the prototypical example of a Ramsey space. The conn
ection between Ramsey spaces\, ultrafilters\, and ideals has been explored
in different ways. Ramsey spaces theory has shown to be crucial to inves
tigate Tukey order\, Karetov order\, and combinatorial properties. This is
why we investigate which ideals are related to a Ramsey space in the same
sense that the ideal Fin is related to the Ellentuck space. In this talk\
, we present some results obtained.\n
LOCATION:https://researchseminars.org/talk/ModelsandSets/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Silvia Barbina (The Open University)
DTSTART;VALUE=DATE-TIME:20210324T134500Z
DTEND;VALUE=DATE-TIME:20210324T150000Z
DTSTAMP;VALUE=DATE-TIME:20230208T070133Z
UID:ModelsandSets/10
DESCRIPTION:Title: Model theory of Steiner triple systems\nby Silvia Barbina (The
Open University) as part of Leeds Models and Sets\n\n\nAbstract\nA Steiner
triple system (STS) is a set together with a collection B of subsets of s
ize 3 such that any two elements of the set belong to exactly one subset i
n B. Finite STSs are well known combinatorial objects for which the litera
ture is extensive. Far fewer results have been obtained on their infinite
counterparts\, which are natural candidates for model-theoretic investigat
ion. I shall review some constructions of infinite STSs\, including the Fr
aïssé limit of the class of finite STSs. I will then give an axiomatisat
ion of the theory of the Fraïssé limit and describe some of its properti
es. This is joint work with Enrique Casanovas.\n
LOCATION:https://researchseminars.org/talk/ModelsandSets/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marlene Koelbing (Universität Wien)
DTSTART;VALUE=DATE-TIME:20210303T134500Z
DTEND;VALUE=DATE-TIME:20210303T150000Z
DTSTAMP;VALUE=DATE-TIME:20230208T070133Z
UID:ModelsandSets/11
DESCRIPTION:Title: Distributivity spectrum of forcing notions\nby Marlene Koelbing
(Universität Wien) as part of Leeds Models and Sets\n\n\nAbstract\nIn my
talk\, I will introduce two different notions of a spectrum of distributi
vity of forcings.\n \nThe first one is the fresh function spectrum\, which
is the set of regular cardinals lambda\, such that the forcing adds a new
function with domain lambda all whose initial segments are in the ground
model. I will provide several examples as well as general facts how to com
pute the fresh function spectrum\, also discussing what sets are realizabl
e as a fresh function spectrum of a forcing.\n \nThe second notion is the
combinatorial distributivity spectrum\, which is the set of possible regul
ar heights of refining systems of maximal antichains without common refine
ment. We discuss the relation between the fresh function spectrum and the
combinatorial distributivity spectrum. We consider the special case of P(o
mega)/fin (for which h is the minimum of the spectrum)\, and use a forcing
construction to show that it is consistent that the combinatorial distrib
utivity spectrum of P(omega)/fin contains more than one element.\n \nThis
is joint work with Vera Fischer and Wolfgang Wohofsky.\n
LOCATION:https://researchseminars.org/talk/ModelsandSets/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justine Falque (Université Paris-Sud)
DTSTART;VALUE=DATE-TIME:20210428T144500Z
DTEND;VALUE=DATE-TIME:20210428T160000Z
DTSTAMP;VALUE=DATE-TIME:20230208T070133Z
UID:ModelsandSets/12
DESCRIPTION:Title: Classification of oligomorphic groups with polynomial profiles\, co
njectures of Cameron and Macpherson.\nby Justine Falque (Université P
aris-Sud) as part of Leeds Models and Sets\n\n\nAbstract\nLet G be a group
of permutations of a denumerable set E. The profile of G is the function
f which counts\, for each n\, the (possibly infinite) number f(n) of orbit
s of G acting on the n-subsets of E. When f takes only finite values\, G i
s called oligomorphic.\n\n\nCounting functions arising this way\, and thei
r associated generating series\, form a rich yet apparently strongly const
rained class. In particular\, Cameron conjectured in the late seventies th
at\, whenever the profile f(n) is bounded by a polynomial (we say that G i
s P-oligomorphic)\, it is asymptotically equivalent to a polynomial. In 19
85\, Macpherson further asked whether the orbit algebra of G (a graded com
mutative algebra invented by Cameron and whose Hilbert function is f) was
finitely generated.\n\n\nAfter providing some context and definitions of t
he involved objects\, this talk will outline the proof of a classification
result of all (closed) P-oligomorphic groups\, of which the conjectures o
f Cameron and Macpherson are corollaries. The proof exploits classical not
ions from group theory (notably block systems and their lattice properties
)\, commutative algebra\, and invariant theory. This research was a joint
work with Nicolas Thiéry.\n
LOCATION:https://researchseminars.org/talk/ModelsandSets/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natasha Dobrinen (University of Denver)
DTSTART;VALUE=DATE-TIME:20210505T164500Z
DTEND;VALUE=DATE-TIME:20210505T180000Z
DTSTAMP;VALUE=DATE-TIME:20230208T070133Z
UID:ModelsandSets/13
DESCRIPTION:Title: Ramsey theory on infinite structures\nby Natasha Dobrinen (Univ
ersity of Denver) as part of Leeds Models and Sets\n\n\nAbstract\nThe Infi
nite Ramsey Theorem says that for any positive integer n\, given a colorin
g of all n-element subsets of the natural numbers into finitely many color
s\, there is an infinite set M of natural numbers such that all n-element
subsets of M have the same color. Infinite Structural Ramsey Theory is co
ncerned with finding analogues of the Infinite Ramsey Theorem for Fraisse
limits\, and also more generally for universal structures. In most cases\
, the exact analogue of Ramsey’s Theorem fails. However\, sometimes one
can find bounds of the following sort: Given a finite substructure A of
an infinite structure S\, we let T(A\,S) denote the least number\, if it e
xists\, such that for any coloring of the copies of A in S into finitely m
any colors\, there is a substructure S’ of S\, isomorphic to S\, such th
at the copies of A in S’ take no more than T(A\,S) colors. If for each
finite substructure A of S\, this number T(A\,S) exists\, then we say that
S has “finite big Ramsey degrees”.\n\nIn the past six years\, there h
as been a resurgence of investigations into the existence and characteriza
tion of big Ramsey degrees for infinite structures\, leading to many new a
nd exciting results and methods. We will present an overview of the area
and some highlights of recent work by various author combinations from amo
ng Balko\, Barbosa\, Chodounsky\, Coulson\, Dobrinen\, Hubicka\, Konjecny\
, Masulovic\, Nesetril\, Patel\, Vena\, and Zucker.\n
LOCATION:https://researchseminars.org/talk/ModelsandSets/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ibrahim Mohammed (University of Leeds)
DTSTART;VALUE=DATE-TIME:20210512T134500Z
DTEND;VALUE=DATE-TIME:20210512T150000Z
DTSTAMP;VALUE=DATE-TIME:20230208T070133Z
UID:ModelsandSets/14
DESCRIPTION:Title: Hyperlogarithmic contraction groups\nby Ibrahim Mohammed (Unive
rsity of Leeds) as part of Leeds Models and Sets\n\n\nAbstract\nContractio
n groups are a model theoretic structure introduced by F.V Kuhlmann to hel
p generalise the global behaviour of the logarithmic function on a non-arc
himedean field. They consist of an ordered abelian group augmented with a
map called the contraction which collapses entire archimedean classes to a
single point. Kuhlmann proved in his paper that the theory of a particula
r type of contraction group had quantifier elimination and was weakly o-mi
nimal (so every definable set is the finite union of convex sets and point
s).\n\nWe can go further and ask how a hyperlogarithmic function behaves g
lobally on a non-archimedean field. A hyper logarithm is the inverse of a
trans exponential\, which is any function that grows faster than all power
s of exp. From an appropriate field equipped with a hyperlogarithm\, we ge
t a new type of structure with two contraction maps\, which we will call '
Hyperlogarithmic contraction groups'. In this talk I will show how the pro
of for Q.E and weak o-minimality given by Kuhlmann can be adapted to show
that Hyperlogrithmic contraction groups also have these properties.\n
LOCATION:https://researchseminars.org/talk/ModelsandSets/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dorottya Sziráki (Alfréd Rényi Institute of Mathematics)
DTSTART;VALUE=DATE-TIME:20210519T134500Z
DTEND;VALUE=DATE-TIME:20210519T150000Z
DTSTAMP;VALUE=DATE-TIME:20230208T070133Z
UID:ModelsandSets/15
DESCRIPTION:Title: The open dihypergraph dichotomy and the Hurewicz dichotomy for gene
ralized Baire spaces\nby Dorottya Sziráki (Alfréd Rényi Institute o
f Mathematics) as part of Leeds Models and Sets\n\n\nAbstract\nGeneralized
descriptive set theory studies analogues\, associated to uncountable regu
lar cardinals $\\kappa$\, of well known topological spaces such as the rea
l line\, the Cantor space and the Baire space. A canonical example is the
generalized Baire space ${}^\\kappa\\kappa$ of functions $f:\\kappa\\to\\k
appa$ equipped with the ${<}\\kappa$-support topology. The open graph dich
otomy for a given set $X$ of reals is a strengthening of the perfect set p
roperty for $X$\, and it can also be viewed as the definable version of th
e open coloring axiom restricted to $X$. Rapha\\"el Carroy\, Benjamin Mill
er and D\\'aniel Soukup have recently introduced an $\\aleph_0$-dimensiona
l generalization of the open graph dichotomy which implies several well-kn
own dichotomy theorems for Polish spaces.\n\nWe show that in Solovay's mod
el\, this $\\aleph_0$-dimensional open dihypergraph dichotomy holds for al
l sets of reals. In our main theorem\, we obtain a version of this previou
s result for generalized Baire spaces ${}^\\kappa\\kappa$ for uncountable
regular cardinals $\\kappa$. As an application\, we derive several version
s of the Hurewicz dichotomy for definable subsets of ${}^\\kappa\\kappa$.
This is joint work with Philipp Schlicht.\n
LOCATION:https://researchseminars.org/talk/ModelsandSets/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nam Trang (University of California\, Irvine)
DTSTART;VALUE=DATE-TIME:20210526T164500Z
DTEND;VALUE=DATE-TIME:20210526T180000Z
DTSTAMP;VALUE=DATE-TIME:20230208T070133Z
UID:ModelsandSets/16
DESCRIPTION:Title: Sealing of the Universally Baire sets\nby Nam Trang (University
of California\, Irvine) as part of Leeds Models and Sets\n\n\nAbstract\nA
set of reals is universally Baire if all of its continuous preimages in t
opological spaces have the Baire property. Sealing is a type of generic ab
soluteness\ncondition introduced by H. W. Woodin that asserts in strong te
rms that the theory of\nthe universally Baire sets cannot be changed by se
t forcings. The Largest Suslin Axiom (LSA) is a determinacy axiom isolated
by Woodin. It as-\nserts that the largest Suslin cardinal is inaccessible
for ordinal definable bijections. \nLSA-over-uB is the statement that in
all (set) generic extensions there is a model of\nLSA whose Suslin\, co-Su
slin sets are the universally Baire sets.\n\nThe main result connecting th
ese notions is: over some mild large cardinal theory\,\nSealing is equicon
sistent with LSA-over-uB. As a consequence\, we obtain that\nSealing is we
aker than the theory “ZFC+there is a Woodin cardinal which is a limit\no
f Woodin cardinals”. This significantly improves upon the earlier consis
tency proof\nof Sealing by Woodin and shows that Sealing is not a strong c
onsequence of\nsupercompactness as suggested by Woodin’s result.\n\nWe d
iscuss some history that leads up to these results as well as the role the
se\nnotions and results play in recent developments in descriptive inner m
odel theory\, an\nemerging field in set theory that explores deep connecti
ons between descriptive set\ntheory\, in particular\, the study of canonic
al models of determinacy and its HOD\, and\ninner model theory\, the study
of canonical inner models of large cardinals. Time permitted\, we will sk
etch proofs of some of the results.\n\nThis talk is based on joint work wi
th G. Sargsyan.\n
LOCATION:https://researchseminars.org/talk/ModelsandSets/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jing Zhang (Bar-Ilan University)
DTSTART;VALUE=DATE-TIME:20210602T134500Z
DTEND;VALUE=DATE-TIME:20210602T150000Z
DTSTAMP;VALUE=DATE-TIME:20230208T070133Z
UID:ModelsandSets/17
DESCRIPTION:Title: When does compactness imply guessing?\nby Jing Zhang (Bar-Ilan
University) as part of Leeds Models and Sets\n\n\nAbstract\nLarge cardinal
properties\, or more generally compactness principles\, usually give rise
to certain guessing principles. For example\, if kappa is measurable\, th
en the diamond principle at kappa holds and if kappa is supercompact\, the
n the Laver diamond principle holds. It is a long-standing open question w
hether weak compactness is consistent with the failure of diamond. In the
80’s\, Woodin showed it is consistent that diamond fails at a greatly Ma
hlo cardinal\, based on the analysis on Radin forcing. It turns out that t
his method cannot yield significant improvement to Woodin’s result. In p
articular\, we show that in any Radin forcing extension with respect to a
measure sequence on kappa\, if kappa is weakly compact\, then the diamond
principle at kappa holds. Despite the negative result\, there are still so
me positive results obtained by refining the analysis of Radin forcing\, d
emonstrating that diamond can fail at a strongly inaccessible cardinal sat
isfying strong compactness properties. Joint work with Omer Ben-Neria.\n
LOCATION:https://researchseminars.org/talk/ModelsandSets/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vahagn Aslanyan (University of East Anglia)
DTSTART;VALUE=DATE-TIME:20210609T134500Z
DTEND;VALUE=DATE-TIME:20210609T150000Z
DTSTAMP;VALUE=DATE-TIME:20230208T070133Z
UID:ModelsandSets/18
DESCRIPTION:Title: A geometric approach to some systems of exponential equations\n
by Vahagn Aslanyan (University of East Anglia) as part of Leeds Models and
Sets\n\n\nAbstract\nI will discuss three important conjectures on complex
exponentiation\, namely\, Schanuel’s conjecture\, Zilber’s Exponentia
l Algebraic Closedness (EAC) conjecture and Zilber’s quasiminimality con
jecture\, and explain how those conjectures are related to each other and
to the model theory of complex exponentiation. I will mainly focus on the
EAC conjecture which states that certain systems of exponential equations
have complex solutions. Then I will show how it can be verified for system
s of exponential equations with dominant additive projection for abelian v
arieties. All the necessary concepts related to abelian varieties will be
defined in the talk. The analogous problem for algebraic tori (i.e. for us
ual complex exponentiation) was solved earlier by Brownawell and Masser. I
f time permits\, I will show how our method can be used to give a new proo
f of their result. This is joint work with Jonathan Kirby and Vincenzo Man
tova.\n
LOCATION:https://researchseminars.org/talk/ModelsandSets/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylvy Anscombe (Institut de Mathématiques de Jussieu-Paris Rive G
auche)
DTSTART;VALUE=DATE-TIME:20210616T134500Z
DTEND;VALUE=DATE-TIME:20210616T150000Z
DTSTAMP;VALUE=DATE-TIME:20230208T070133Z
UID:ModelsandSets/19
DESCRIPTION:Title: Some existential theories of fields\nby Sylvy Anscombe (Institu
t de Mathématiques de Jussieu-Paris Rive Gauche) as part of Leeds Models
and Sets\n\n\nAbstract\nBuilding on previous work\, I will discuss Turing
reductions between various fragments of theories of fields. In particular\
, we exhibit several theories of fields Turing equivalent to the existenti
al theory of the rational numbers. This is joint work with Arno Fehm.\n
LOCATION:https://researchseminars.org/talk/ModelsandSets/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jinhe (Vincent) Ye (Institut de Mathématiques de Jussieu-Paris Ri
ve Gauche)
DTSTART;VALUE=DATE-TIME:20210623T124500Z
DTEND;VALUE=DATE-TIME:20210623T140000Z
DTSTAMP;VALUE=DATE-TIME:20230208T070133Z
UID:ModelsandSets/20
DESCRIPTION:Title: The étale open topology and the stable fields conjecture\nby J
inhe (Vincent) Ye (Institut de Mathématiques de Jussieu-Paris Rive Gauche
) as part of Leeds Models and Sets\n\n\nAbstract\nFor any field $K$\, we i
ntroduce natural topologies on $K$-points of varieties over $K$\, which is
defined to be the weakest topology such that étale morphisms are open. T
his topology turns out to be natural in a lot of settings. For example\, w
hen $K$ is algebraically closed\, it is easy to see that we have the Zaris
ki topology\, and the procedure picks up the valuation topology in many he
nselian valued fields. Moreover\, many topological properties correspond t
o the algebraic properties of the field. As an application of this corresp
ondence\, we will show that large stable fields are separably closed. Join
t work with Will Johnson\, Chieu-Minh Tran\, and Erik Walsberg.\n
LOCATION:https://researchseminars.org/talk/ModelsandSets/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Adam-Day (University of Oxford)
DTSTART;VALUE=DATE-TIME:20211013T124500Z
DTEND;VALUE=DATE-TIME:20211013T140000Z
DTSTAMP;VALUE=DATE-TIME:20230208T070133Z
UID:ModelsandSets/21
DESCRIPTION:Title: Rigid branchwise-real tree orders\nby Sam Adam-Day (University
of Oxford) as part of Leeds Models and Sets\n\n\nAbstract\nA branchwise-re
al tree order is a partial order tree in which every branch is isomorphic
to a real interval. In this talk\, I give several methods of constructing
examples of these which are rigid (i.e. without non-trivial automorphisms)
\, subject to increasing uniformity conditions. I show that there is a rig
id branchwise-real tree order in which every branching point has the same
degree\, one in which every point is branching and of the same degree\, an
d finally one in which every point is branching of the same degree and whi
ch admits no monotonic function into the reals. Trees are grown iterativel
y in stages\, and a key technique is the construction (in ZFC) of a family
of colourings of (0\,infty) which is 'sufficiently generic'\, using these
colourings to determine how to proceed with the construction.\n
LOCATION:https://researchseminars.org/talk/ModelsandSets/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mirna Džamonja (CNRS – Université de Paris)
DTSTART;VALUE=DATE-TIME:20211020T124500Z
DTEND;VALUE=DATE-TIME:20211020T140000Z
DTSTAMP;VALUE=DATE-TIME:20230208T070133Z
UID:ModelsandSets/22
DESCRIPTION:Title: On the universality problem for $\\aleph_2$-Aronszajn and wide $\\a
leph_2$ Aronszajn trees\nby Mirna Džamonja (CNRS – Université de P
aris) as part of Leeds Models and Sets\n\n\nAbstract\nWe report on a joint
work in progress with Rahman Mohammadpour in which we study the problem o
f the possible existence of a universal tree under weak embeddings in the
classes of $\\aleph_2$-Aronszajn and wide $\\aleph_2$-Aronszajn trees. Thi
s problem is more complex than previously thought\, in particular it seems
not to be resolved under ShFA + CH using the technology of weakly Lipshit
z trees. We show that under CH\, for a given $\\aleph_2$-Aronszajn tree T
without a weak ascent path\, there is an $\\aleph_2$-cc countably closed f
orcing forcing which specialises T and adds an $\\aleph_2$-Aronszajn tree
which does not embed into T. One cannot however apply the ShFA to this for
cing.\n\nFurther\, we construct a model à la Laver-Shelah in which there
are $\\aleph_2$-Aronszajn trees\, but none is universal. Work in progress
is to obtain an analogue for universal wide $\\aleph_2$-Aronszajn trees. W
e also comment on some negative ZFC results in the case that the embedding
s are assumed to have a strong preservation property.\n
LOCATION:https://researchseminars.org/talk/ModelsandSets/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dilip Raghavan (National University of Singapore)
DTSTART;VALUE=DATE-TIME:20211027T144500Z
DTEND;VALUE=DATE-TIME:20211027T160000Z
DTSTAMP;VALUE=DATE-TIME:20230208T070133Z
UID:ModelsandSets/23
DESCRIPTION:Title: Galvin’s problem in higher dimensions\nby Dilip Raghavan (Nat
ional University of Singapore) as part of Leeds Models and Sets\n\n\nAbstr
act\nThis talk will discuss recent work on Galvin's conjecture in Ramsey t
heory. I will review the background and discuss previous work on the two d
imensional case before focusing on the recent work on dimensions greater t
han 2. This is joint work with Stevo Todorcevic.\n
LOCATION:https://researchseminars.org/talk/ModelsandSets/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katrin Tent (Westfälische Wilhelms-Universität Münster)
DTSTART;VALUE=DATE-TIME:20211103T134500Z
DTEND;VALUE=DATE-TIME:20211103T150000Z
DTSTAMP;VALUE=DATE-TIME:20230208T070133Z
UID:ModelsandSets/24
DESCRIPTION:by Katrin Tent (Westfälische Wilhelms-Universität Münster)
as part of Leeds Models and Sets\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ModelsandSets/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victoria Gitman (CUNY Graduate Center)
DTSTART;VALUE=DATE-TIME:20211110T134500Z
DTEND;VALUE=DATE-TIME:20211110T150000Z
DTSTAMP;VALUE=DATE-TIME:20230208T070133Z
UID:ModelsandSets/25
DESCRIPTION:Title: Set theory without powerset\nby Victoria Gitman (CUNY Graduate
Center) as part of Leeds Models and Sets\n\n\nAbstract\nMany natural set-t
heoretic structures satisfy the basic axioms of set theory\, but not the p
owerset axiom. These include the collections $H_{\\kappa^+}$ of sets whose
transitive closure has size at most $\\kappa$\, forcing extensions of mod
els of ${\\rm ZFC}$ by pretame (but not tame) forcing\, and first-order mo
dels that are morally equivalent to models of the second-order Kelley-Mors
e set theory (with class choice). It turns out that a reasonable set theor
y in the absence of the powerset axiom is not simply ${\\rm ZFC}$ with the
powerset axiom removed. Without the powerset axiom\, the Replacement sche
me is not equivalent to the Collection scheme\, and the various forms of t
he Axiom of Choice are not equivalent. In this talk\, I will give an overv
iew of the properties of a robust set theory without powerset\, ${\\rm ZFC
}^-$\, whose axioms are ${\\rm ZFC}$ without the powerset axiom\, with the
Collection scheme instead of the Replacement scheme and the Well-Ordering
Principle instead of the Axiom of Choice. While a great deal of standard
set theory can be carried out in ${\\rm ZFC}^-$\, for instance\, forcing w
orks mostly as it does in ${\\rm ZFC}$\, there are several important prope
rties that are known to fail and some which we still don't know whether th
ey hold. For example\, the Intermediate Model Theorem fails for ${\\rm ZFC
}^-$\, and so does ground model definability\, and it is not known whether
${\\rm HOD}$ is definable. I will also discuss a strengthening of ${\\rm
ZFC}^-$ obtained by adding the Dependent Choice Scheme\, and some rather s
trange ${\\rm ZFC}^-$-models.\n
LOCATION:https://researchseminars.org/talk/ModelsandSets/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monica VanDieren (Robert Morris University)
DTSTART;VALUE=DATE-TIME:20211117T134500Z
DTEND;VALUE=DATE-TIME:20211117T150000Z
DTSTAMP;VALUE=DATE-TIME:20230208T070133Z
UID:ModelsandSets/26
DESCRIPTION:Title: Twenty Years of Tameness\nby Monica VanDieren (Robert Morris Un
iversity) as part of Leeds Models and Sets\n\n\nAbstract\nIn the 1970s Sah
aron Shelah initiated a program to develop classification theory for non-e
lementary classes\, and eventually settled on the setting of abstract elem
entary classes. For over three decades\, limited progress was made\, most
of which required additional set theoretic axioms. In 2001\, Rami Grossbe
rg and I introduced the model theoretic concept of tameness which opened t
he door for stability results in abstract elementary classes in ZFC. Duri
ng the following 20 years\, tameness along with limit models have been use
d by several mathematicians to prove categoricity theorems and to develop
non-first order analogs to forking calculus and stability theory\, solving
a very large number of problems posed by Shelah in ZFC. Recently\, Marcus
Mazari-Armida found applications to Abelian group theory and ring theory.
In this presentation I will highlight some of the more surprising result
s involving tameness and limit models.\n
LOCATION:https://researchseminars.org/talk/ModelsandSets/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noa Lavi (Politecnico di Torino)
DTSTART;VALUE=DATE-TIME:20211125T134500Z
DTEND;VALUE=DATE-TIME:20211125T150000Z
DTSTAMP;VALUE=DATE-TIME:20230208T070133Z
UID:ModelsandSets/27
DESCRIPTION:by Noa Lavi (Politecnico di Torino) as part of Leeds Models an
d Sets\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ModelsandSets/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Postponed to 15th December due to strike action
DTSTART;VALUE=DATE-TIME:20211201T134500Z
DTEND;VALUE=DATE-TIME:20211201T150000Z
DTSTAMP;VALUE=DATE-TIME:20230208T070133Z
UID:ModelsandSets/28
DESCRIPTION:by Postponed to 15th December due to strike action as part of
Leeds Models and Sets\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ModelsandSets/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anush Tserunyan (McGill University)
DTSTART;VALUE=DATE-TIME:20211208T134500Z
DTEND;VALUE=DATE-TIME:20211208T150000Z
DTSTAMP;VALUE=DATE-TIME:20230208T070133Z
UID:ModelsandSets/29
DESCRIPTION:by Anush Tserunyan (McGill University) as part of Leeds Models
and Sets\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ModelsandSets/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aris Papadopoulos (University of Leeds)
DTSTART;VALUE=DATE-TIME:20211215T134500Z
DTEND;VALUE=DATE-TIME:20211215T150000Z
DTSTAMP;VALUE=DATE-TIME:20230208T070133Z
UID:ModelsandSets/30
DESCRIPTION:Title: Around Generalised Indiscernibles and Higher-arity Independence Pro
perties\nby Aris Papadopoulos (University of Leeds) as part of Leeds M
odels and Sets\n\n\nAbstract\nThe machinery of generalised indiscernibles
has played a key role in recent developments of stability theory. One of t
he most important applications of this machinery is characterising dividin
g lines by collapsing indiscernibles\, a programme essentially tracing bac
k to the early work of Shelah in the 1980s which has seen a resurgence lat
ely\, starting with the work of Scow.\nIn my talk\, I will survey the main
definitions and some important notions concerning these generalised indis
cernibles and give some examples of characterising dividing lines by colla
psing indiscernibles. Finally\, if time permits\, I will discuss an applic
ation of generalised indiscernibles to higher-arity independence propertie
s\, showing that IP_k can be witnessed by formulas in singleton variables
if one allows parameters (from some model).\n
LOCATION:https://researchseminars.org/talk/ModelsandSets/30/
END:VEVENT
END:VCALENDAR