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SUMMARY:Ruiyuan Chen (U Illinois Urbana-Champaign)
DTSTART:20200702T180000Z
DTEND:20200702T190000Z
DTSTAMP:20260423T021241Z
UID:OLS/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OLS/15/">Sto
 ne duality and strong conceptual completeness for infinitary logic</a>\nby
  Ruiyuan Chen (U Illinois Urbana-Champaign) as part of Online logic semina
 r\n\n\nAbstract\nThe classical Stone duality\, applied to the Lindenbaum-T
 arski\nalgebra of a propositional theory\, allows the syntax of the theory
  to be\ncanonically recovered from its space of models\; this encompasses 
 both\nthe completeness and definability theorems for propositional logic.\
 nMany known variants and generalizations of Stone duality have analogous\n
 interpretations as completeness-definability theorems for various\nfragmen
 ts of finitary propositional and first-order logic.  In this\ntalk\, I wil
 l give an overview of this duality-theoretic approach to\ncompleteness\, i
 ncluding the key examples of Stone duality as well as\nMakkai duality for 
 first-order logic.  I will then present a duality\ntheorem for the countab
 ly infinitary first-order logic\n$L_{\\omega_1\\omega}$\, proved using too
 ls from invariant descriptive set\ntheory as well as topos theory.\n
LOCATION:https://researchseminars.org/talk/OLS/15/
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