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UID:5e0a15f48c2be077829126@ist.ac.at
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DESCRIPTION:Speaker: Sebastien Vasey\nhosted by Tim Browning\nAbstract: Abs
tract: Ramsey's theorem says that for each natural number n\, there exists
a natural number N so that each graph with N vertices contains either a c
lique or an independent set of size n. A theorem of Erd?s and Rado general
izes it to infinite cardinals. Ramsey himself showed that one can take n =
N if n is the first infinite cardinal but in most other uncountable cases
N must be much bigger than n. Stability theory is a branch of model theor
y studying certain definability conditions allowing us to take n = N for a
large number of infinite cardinals. Historically\, stability theory was f
irst developed by Shelah for classes axiomatized by first-order formulas.
In this talk\, I will describe a generalization to a large class of concre
te categories: abstract elementary classes. I will also talk about recent
progresses on the field's main test question\, the eventual categoricity c
onjecture\, resolved by Morley and Shelah for first-order but still open f
or abstract elementary classes.
LOCATION:Mondi Seminar Room 2\, Central Building\, IST Austria
ORGANIZER:tguggenb@ist.ac.at
SUMMARY:Stability theory for concrete categories
URL:https://talks-calendar.app.ist.ac.at/events/2464
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