Date/Time
Date(s) - 12/01/2026
12:30 pm - 1:30 pm

Speaker: Biran Falk-Dotan (Hebrew University)

Location: Hamilton Hall, Room 410

Title: Definable Automorphisms and Compact Quantifiers

Abstract: Mostowski (1957) asked: Can 1st order logic be extended by 2nd order quantifiers while preserving the compactness theorem? The present work, with Saharon Shelah, shows sufficient conditions for compactness of quantification over automorphisms. We achieve this by adapting the method of Keisler (1970) to construct an elementary chain of models which omits a sequence of types, thus “blocking” the “undesirable” automorphisms. The method works for interpretations of unstable theories with an appropriate notion of bigness (will be defined in the talk). The “cost” is assuming the diamond principle for some cardinals. We apply the result to some well-known theories and, if time allows, discuss more generally how one might apply the result to new theories.