November 5
Piotr Gruza,
University of Warsaw
Separations between categoricity-like properties of first-order theories
A theory is tight if and only if every two extensions of it, in the language of that theory, are bi-interpretable iff they are equal. The property of being tight can be seen as a kind of local categoricity in a suitable category of theories and interpretations. Examples of tight theories include $\text{PA}$, $\text{Z}_{2}$, $\text{ZF}$, and $\text{KM}$. Neatness, semantic tightness, and solidity are strengthenings of tightness, with solidity being the strongest and the other two being intermediate. During the talk we will focus on relations between those properties in the context of arithmetic theories and theories of finite sets.
Partly based on a joint work with Leszek Kołodziejczyk and Mateusz Łełyk.