Date:
Wed, 26/06/202411:15-13:15
Location:
Ross 70
Join Zoom Meeting
https://huji.zoom.us/j/84185540747?pwd=62WsNN8O2tjtAvQ9nljbu9gMb5m9s8.1
Title: Compactness of logics with quantification over automorphisms
Abstract: Proper extensions of first-order logic by second-order quantifiers cannot satisfy both the compactness and Löwenheim-Skolem theorems, and might not even satisfy one of them. However, some second-order quantifiers have been shown to satisfy compactness, including quantification over automorphisms of (definable) Boolean algebras and isomorphisms of (definable) ordered fields. The present goal is to expand these results to more general structures, even at the expense of using ZFC-independent assumptions such as the diamond principle. This talk will discuss the method of Mekler & Shelah (1993) for proving compactness from ZFC (using a Black Box) and its possible generalization for quantification over various other structures.
https://huji.zoom.us/j/84185540747?pwd=62WsNN8O2tjtAvQ9nljbu9gMb5m9s8.1
Title: Compactness of logics with quantification over automorphisms
Abstract: Proper extensions of first-order logic by second-order quantifiers cannot satisfy both the compactness and Löwenheim-Skolem theorems, and might not even satisfy one of them. However, some second-order quantifiers have been shown to satisfy compactness, including quantification over automorphisms of (definable) Boolean algebras and isomorphisms of (definable) ordered fields. The present goal is to expand these results to more general structures, even at the expense of using ZFC-independent assumptions such as the diamond principle. This talk will discuss the method of Mekler & Shelah (1993) for proving compactness from ZFC (using a Black Box) and its possible generalization for quantification over various other structures.