Date:
Wed, 22/10/202511:00-13:00
Location:
Ross 70
Zoom link: https://huji.zoom.us/j/83723267432?pwd=uRqaskH0WskEvavHF0l19WO1FXxb8v.1
Meeting ID: 837 2326 7432
Passcode: 440298
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?
This work, supervised by Saharon Shelah, shows sufficient conditions for compactness of quantification over automorphisms. We achieve this by adapting the method of Keisler (1971) to construct an elementary chain of models which omits a sequence of types. 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.
Finally, we apply the result to some well-known theories.
Meeting ID: 837 2326 7432
Passcode: 440298
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?
This work, supervised by Saharon Shelah, shows sufficient conditions for compactness of quantification over automorphisms. We achieve this by adapting the method of Keisler (1971) to construct an elementary chain of models which omits a sequence of types. 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.
Finally, we apply the result to some well-known theories.