Online seminář z algebry - 30.4.2020 PDF Tisk

Další seminář z algebry se koná 30.4.2020 od 13.00 online na platformě ZOOM. Informace pro připojení a další program semináře je zde.

Christian Espindola

A topos theoretic proof of Shelah’s eventual categoricity conjecture

Assuming the Generalized Continuum Hypothesis (GCH), we give a topos-theoretic proof of Shelah's eventual categoricity conjecture for abstract elementary classes (AEC) with amalgamation. The proof is based on infinitary generalizations of Deligne and Joyal's completeness theorems for certain infinitary intuitionistic logics, by means of which it is possible to attack the question of categoricity in a topos-theoretic way. Using recent results on the Scott adjunction developed by Henry and Di Liberti, we prove under GCH that an AEC with amalgamation which is categorical in a pair of cardinals is also categorical in all cardinals in between. Under some extra natural assumptions on the AEC, we also deduce a new downward categoricity transfer. We also explain how these methods can be adapted to shed some light on the categoricity spectrum of more general accessible categories.

Aktualizováno Pátek, 24 Duben 2020 09:52