Model Theory Seminar

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