4 papers
Linear Orders in Presburger Arithmetic
Fedor Pakhomov, Alexander Zapryagaev
We prove the linear orders first-order definable in the standard model $(\ZZ;<,+)$ of Presburger arithmetic are exactly those that are $(\ZZ;<,+)$-definably embeddable into the lex…
Multi-Dimensional Interpretations of Presburger Arithmetic in Itself
Fedor Pakhomov, Alexander Zapryagaev
Presburger Arithmetic is the true theory of natural numbers with addition. We study interpretations of Presburger Arithmetic in itself. The main result of this paper is that all se…
Interpretations of Linear Orderings in Presburger Arithmetic
Alexander Zapryagaev
Presburger Arithmetic is the true theory of natural numbers with addition. We consider linear orderings interpretable in Presburger Arithmetic and…
Interpretations of Presburger Arithmetic in Itself
Alexander Zapryagaev, Fedor Pakhomov
Presburger arithmetic PrA is the true theory of natural numbers with addition. We study interpretations of PrA in itself. We prove that all one-dimensional self-interpretations are…