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# Model Theory Seminar

Thursday, February 7, 2019 — 4:00 PM EST

Abolfazl Alam, Shahid Beheshti University

"Model Companion for Bounded Theories and some Related Complexity Questions"

A theory $T$ is called bounded model complete (b.m.c for short) if whenever $M\subseteq N$ are models of $T$, then $M\subseteq_1^b N$. In the language of bounded arithmetic, a bounded theory $T$ ‎is bounded model complete if and only if $T$ satisfies $\rm NP=coNP$. I describe the notion of bounded model companion and try to find the bounded model companion for some well-known bounded theories in bounded arithmetic such as $\rm S_{2‎}^{1}$.

MC 5403

### July 2020

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