On Interpretations in B\"uchi Arithmetics
Logic
2022-11-30 v1
Abstract
B\"uchi arithmetics BA_n, n >= 2, are extensions of Presburger arithmetic with an unary functional symbol V_n(x) denoting the largest power of n that divides x. Definability of a set in BA_n is equivalent to its recognizability by a finite automaton receiving numbers in their n-ary expansion. We show that B\"uchi arithmetics BA_n and BA_m are bi-interpretable for any n,m. Furthermore, we establish that any interpretation of some structure in BA_n is isomorphic to some one-dimensional interpretation; however, this isomorphism must not be BA_n-definable.
Cite
@article{arxiv.2211.16392,
title = {On Interpretations in B\"uchi Arithmetics},
author = {Alexnader Zapryagaev},
journal= {arXiv preprint arXiv:2211.16392},
year = {2022}
}