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BEGIN:VEVENT
SUMMARY:Victoria Gitman (City University of New York)
DTSTART:20200506T150000Z
DTEND:20200506T163000Z
DTSTAMP:20260422T215251Z
UID:oxford-set-theory/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/oxford-set-t
 heory/1/">Elementary embeddings and smaller large cardinals</a>\nby Victor
 ia Gitman (City University of New York) as part of Oxford Set Theory Semin
 ar\n\nLecture held in Online\, via Zoom.\n\nAbstract\nA common theme in th
 e definitions of larger large cardinals is the existence of elementary emb
 eddings from the universe into an inner model. In contrast\, smaller large
  cardinals\, such as weakly compact and Ramsey cardinals\, are usually cha
 racterized by their combinatorial properties such as existence of large ho
 mogeneous sets for colorings. It turns out that many familiar smaller larg
 e cardinals have elegant elementary embedding characterizations. The embed
 dings here are correspondingly 'small'\;&nbsp\;they are between transitive
  set models of set theory\, usually the size of the large cardinal in ques
 tion. The study of these elementary embeddings has led us to isolate certa
 in important properties via which we have defined robust hierarchies of la
 rge cardinals below a measurable cardinal. In this talk\, I will introduce
  these types of elementary embeddings and discuss the large cardinal hiera
 rchies that have come out of the analysis of their properties. The more re
 cent results in this area are a joint work with Philipp Schlicht.\n
LOCATION:https://researchseminars.org/talk/oxford-set-theory/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel David Hamkins (Oxford University)
DTSTART:20200520T150000Z
DTEND:20200520T163000Z
DTSTAMP:20260422T215251Z
UID:oxford-set-theory/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/oxford-set-t
 heory/2/">Bi-interpretation of weak set theories</a>\nby Joel David Hamkin
 s (Oxford University) as part of Oxford Set Theory Seminar\n\n\nAbstract\n
 Set theory exhibits a truly robust mutual interpretability phenomenon: in 
 any model of one set theory we can define models of diverse other set theo
 ries and vice versa. In any model of ZFC\, we can define models of ZFC + G
 CH and also of ZFC + ¬CH and so on in hundreds of cases. And yet\, it tur
 ns out\, in no instance do these mutual interpretations rise to the level 
 of bi-interpretation. Ali Enayat proved that distinct theories extending Z
 F are never bi-interpretable\, and models of ZF are bi-interpretable only 
 when they are isomorphic. So there is no nontrivial bi-interpretation phen
 omenon in set theory at the level of ZF or above.&nbsp\; Nevertheless\, fo
 r natural weaker set theories\, we prove\, including ZFC- without power se
 t and Zermelo set theory Z\, there are nontrivial instances of bi-interpre
 tation. Specifically\, there are well-founded models of ZFC- that are bi-i
 nterpretable\, but not isomorphic---even $\\langle H_{\\omega_1}\,\\in\\ra
 ngle$ and $\\langle H_{\\omega_2}\,\\in\\rangle$ can be bi-interpretable--
 -and there are distinct bi-interpretable theories extending ZFC-. Similarl
 y\, using a construction of Mathias\, we prove that every model of ZF is b
 i-interpretable with a model of Zermelo set theory in which the replacemen
 t axiom fails. This is joint work with Alfredo Roque Freire.\n
LOCATION:https://researchseminars.org/talk/oxford-set-theory/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ali Enayat (Gothenberg)
DTSTART:20200527T150000Z
DTEND:20200527T163000Z
DTSTAMP:20260422T215251Z
UID:oxford-set-theory/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/oxford-set-t
 heory/3/">Leibnizian and anti-Leibnizian motifs in set theory</a>\nby Ali 
 Enayat (Gothenberg) as part of Oxford Set Theory Seminar\n\n\nAbstract\nLe
 ibniz's principle of identity of indiscernibles at first sight appears com
 pletely&nbsp\;unrelated to set theory\, but Mycielski (1995) formulated a 
 set-theoretic axiom&nbsp\;nowadays referred to as LM (for Leibniz-Mycielsk
 i) which captures the spirit of Leibniz's dictum in the&nbsp\;following se
 nse:&nbsp\; LM holds in a model M of ZF iff M is elementarily&nbsp\;equiva
 lent to a model M* in which there is no pair of indiscernibles.&nbsp\; LM 
 was further investigated in a 2004&nbsp\; paper of mine\, which includes a
  proof that LM is equivalent to the global form of the Kinna-Wagner select
 ion principle in set theory.&nbsp\; On the other hand\, one can formulate 
 a strong negation of Leibniz's principle by first adding a unary predicate
  I(x) to the usual language of set theory\, and then augmenting ZF with a 
 scheme that ensures that I(x) describes a proper class of indiscernibles\,
  thus giving rise to an extension ZFI of ZF that I showed (2005) to be int
 imately related to Mahlo cardinals of finite order. In this talk I will gi
 ve an expository account of the above and related results that attest to a
  lively interaction between set theory and Leibniz's principle of identity
  of indiscernibles.\n
LOCATION:https://researchseminars.org/talk/oxford-set-theory/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Corey Bacal Switzer (City University of New York)
DTSTART:20200617T150000Z
DTEND:20200617T163000Z
DTSTAMP:20260422T215251Z
UID:oxford-set-theory/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/oxford-set-t
 heory/4/">Some Set Theory of Kaufmann Models</a>\nby Corey Bacal Switzer (
 City University of New York) as part of Oxford Set Theory Seminar\n\n\nAbs
 tract\nA Kaufmann model is an $\\omega_1$-like\, recursively saturated\, r
 ather classless model of PA. Such models were shown to exist by Kaufmann u
 nder the assumption that $\\diamondsuit$ holds\, and in ZFC by Shelah via 
 an absoluteness argument involving strong logics. They are important in th
 e theory of models of arithmetic notably because they show that many class
 ic results about countable\, recursively saturated models of arithmetic ca
 nnot be extended to uncountable models. They are also a particularly inter
 esting example of set theoretic incompactness at $\\omega_1$\, similar to 
 an Aronszajn tree.</p>\n\n<p>\nIn this talk we’ll look at several set th
 eoretic issues relating to this class of models motivated by the seemingly
  naïve question of whether or not such models can be killed by forcing wi
 thout collapsing $\\omega_1$. Surprisingly the answer to this question tur
 ns out to be independent: under $\\mathsf{MA}_{\\aleph_1}$ no $\\omega_1$-
 preserving forcing can destroy Kaufmann-ness whereas under $\\diamondsuit$
  there is a Kaufmann model $M$ and a Souslin tree $S$ so that forcing with
  $S$ adds a satisfaction class to $M$ (thus killing rather classlessness).
  The techniques involved in these proofs also yield another surprising sid
 e of Kaufmann models: it is independent of ZFC whether the class of Kaufma
 nn models can be axiomatized in the logic $L_{\\omega_1\, \\omega}(Q)$ whe
 re $Q$ is the quantifier “there exists uncountably many”. This is the 
 logic used in Shelah’s aforementioned result\, hence the interest in thi
 s level of expressive power.\n
LOCATION:https://researchseminars.org/talk/oxford-set-theory/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Blass (University of Michigan)
DTSTART:20201021T150000Z
DTEND:20201021T163000Z
DTSTAMP:20260422T215251Z
UID:oxford-set-theory/5
DESCRIPTION:by Andreas Blass (University of Michigan) as part of Oxford Se
 t Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/oxford-set-theory/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mirna Džamonja (INSTITUT FOR HISTORY AND PHILOSOPHY OF SCIENCES A
 ND TECHNIQUES\, CNRS & UNIVERSITÉ PANTHÉON SORBONNE\, PARIS AND INSTITUT
 E OF MATHEMATICS\, CZECH ACADEMY OF SCIENCES\, PRAGUE)
DTSTART:20201104T160000Z
DTEND:20201104T173000Z
DTSTAMP:20260422T215251Z
UID:oxford-set-theory/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/oxford-set-t
 heory/6/">On wide Aronszajn trees</a>\nby Mirna Džamonja (INSTITUT FOR HI
 STORY AND PHILOSOPHY OF SCIENCES AND TECHNIQUES\, CNRS & UNIVERSITÉ PANTH
 ÉON SORBONNE\, PARIS AND INSTITUTE OF MATHEMATICS\, CZECH ACADEMY OF SCIE
 NCES\, PRAGUE) as part of Oxford Set Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/oxford-set-theory/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Goldberg (Harvard University)
DTSTART:20201118T160000Z
DTEND:20201118T173000Z
DTSTAMP:20260422T215251Z
UID:oxford-set-theory/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/oxford-set-t
 heory/7/">Even ordinals and the Kunen inconsistency</a>\nby Gabriel Goldbe
 rg (Harvard University) as part of Oxford Set Theory Seminar\n\nAbstract: 
 TBA\n
LOCATION:https://researchseminars.org/talk/oxford-set-theory/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kameryn J Williams (UNIVERSITY OF HAWAI’I AT MĀNOA)
DTSTART:20201202T160000Z
DTEND:20201202T173000Z
DTSTAMP:20260422T215251Z
UID:oxford-set-theory/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/oxford-set-t
 heory/8/">The geology of inner mantles</a>\nby Kameryn J Williams (UNIVERS
 ITY OF HAWAI’I AT MĀNOA) as part of Oxford Set Theory Seminar\n\nAbstra
 ct: TBA\n
LOCATION:https://researchseminars.org/talk/oxford-set-theory/8/
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