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ON INTERPRETATIONS OF PRESBURGER ARITHMETIC IN BÜCHI ARITHMETICS
- Authors: Zapryagaev A.A.1
-
Affiliations:
- National Research University “Higher School of Economics”
- Issue: Vol 510, No 1 (2023)
- Pages: 3-7
- Section: MATHEMATICS
- URL: https://rjeid.com/2686-9543/article/view/647851
- DOI: https://doi.org/10.31857/S2686954322600641
- EDN: https://elibrary.ru/XHJOFS
- ID: 647851
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Abstract
Büchi arithmetics BAn, \(n \geqslant 2\), 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 BAn is equivalent to its recognizability by a finite automaton receiving numbers in their n-ary expansion. We consider the interpretations of Presburger Arithmetic in the standard model of BAn and show that each such interpretation has an internal model isomorphic to the standard one. This answers a question by A. Visser on the interpretations of certain weak arithmetical theories in themselves.
About the authors
A. A. Zapryagaev
National Research University “Higher School of Economics”
Author for correspondence.
Email: azapryagaev@hse.ru
Russian Federation, Moscow
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