# Logic Seminar - Yatir Halevi

Date:
Wed, 18/05/202211:15-13:00
Location:
https://huji.zoom.us/j/89186499242?pwd=Rjl1czhLeGI1L2dRL1E5RXRrbmIvdz09

Title: Enriching a predicate and tame expansions of the integers

Abstract: Given a structure M and a stably embedded 0-definable set Q, we prove tameness preservation results when enriching the induced structure on Q by some further structure.

In particular, we show that if the original structure and the enriched structure on Q are stable (resp., superstable, ω​​-stable), then so is the induced enrichment of M.

Using these results  we construct the first known examples of strictly stable expansions of (ℤ,+)​​. More generally, we show that any stable (resp., superstable) countable graph can be defined in a stable (resp., superstable) expansion of (ℤ,+)​​ by some unary predicate A⊆ℕ​​.

Joint work with G. Conant, C. d'Elbee, L. Jimenez and S. Rideau-Kikuchi