## Model Theory Seminar - Christopher Hawthorne - Automata and tame expansions of $(\mathbb{Z},+)$

- Calendar
- Mathematics & Statistics

- Date
- 11.13.2020 11:30 am - 12:30 pm

### Description

Title: Automata and tame expansions of $(\mathbb{Z},+)$

Speaker: Christopher Hawthorne (Univ. of Waterloo)

Abstract: In 2018 Palacín and Sklinos posed the general question of which subsets $A$ of$\mathbb{Z}$ produce stable expansions of $(\mathbb{Z},+)$. In this talk, we will consider this question, and an analogous question about NIP, restricted to the context of $d$*-automatic sets*: that is, sets of integers whose set of representations base $d$ is recognized by a finite automaton. Finite automata and the sets recognized thereby are important topics in computer science, and are known to have nice interactions with algebra and logic. We will see that automata theory gives us a nice proof of the recent result of Lambotte and Point that $(\mathbb{Z},+,<,d^{\mathbb{N}})$ is NIP for $d>0$. On the stability-theoretic side, it turns out that the only such $A$that are $d$-automatic are the "F-sets" exhibited by Moosa and Scanlon in 2004.

I won't assume any knowledge of automata theory in this talk.

Location: Virtual

If you need the zoom link for this talk, please contact Bradd Hart