3 papers
math.LO2026
Analogues of Shepherdson's Theorem for a language with exponentiation
Konstantin Kovalyov
In 1964 Shepherdson \cite{shepherdson:1964} proved that a discretely ordered semiring satisfies (quantifier free induction) iff the corresponding ring…
math.LO2026
A natural axiomatization of Büchi Arithmetic
Konstantin Kovalyov
We investigate Büchi Arithmetic -- the elementary theory of the natural numbers equipped with addition and the function mapping a number to the greatest power…
math.LO2024
Axiomatization of Büchi arithmetic
Konstantin Kovalyov
In this paper we introduce an axiomatization of Büchi arithmetic, i.e., of the elementary theory of natural numbers in the language with addition and function such…