Seminars: K. A. Kovalyov, Models of quantifier-free induction for the language of arithmetic with exponentiation

SEMINARS


Seminars "Proof Theory" and "Logic Online Seminar" November 8, 2021 18:30, Moscow, Steklov Mathematical Institute (8 Gubkina), room 313 + online

Models of quantifier-free induction for the language of arithmetic with exponentiation K. A. Kovalyov Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
https://youtu.be/hEL0G8ATawQ Abstract: In 1964 Shepherdson proved the following fact: a discretely ordered semiring $M^+$ satisfies $\mathrm{IOpen}$ (the induction schema for quantifier-free formulas) iff the corresponding ring $M$ is the integer part of the real closure of the quotient field of $M$. ($M$ is called an integer part of $R$ if $M$ is discretely ordered and for all $r$ in $R$ there exists an $m$ in $M$ such that $m \leq r < m+1$.) We consider the expansions of $\mathrm{IOpen}$ with the exponentiation and the power functions and try to find similar criteria to build models of these theories. The talk will be in Russian.