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pro vyhledávání: '"Zapryagaev, Alexander"'
Autor:
Zapryagaev, Alexander
B\"uchi arithmetics $\mathop{\mathbf{BA}}\nolimits_n$, $n\ge 2$, are extensions of Presburger arithmetic with an unary functional symbol $V_n(x)$ denoting the largest power of $n$ that divides $x$. We explore the structure of non-standard models of B
Externí odkaz:
http://arxiv.org/abs/2312.13757
Autor:
Zapryagaev, Alexander
B\"uchi arithmetics $\mathop{\mathbf{BA}}\nolimits_n$, $n\ge 2$, are extensions of Presburger arithmetic with an unary functional symbol $V_n(x)$ denoting the largest power of $n$ that divides $x$. A rank of a linear order is the minimal number of co
Externí odkaz:
http://arxiv.org/abs/2310.16019
Autor:
Pakhomov, Fedor, Zapryagaev, Alexander
We prove that any linear order definable in the standard model (Z, <, +) of Presburger arithmetic is (Z, <, +)-definably embeddable into the lexicographic ordering on Z^n, for some n.
Comment: 15 pages. To be submitted to Proc. Am. Math. Soc
Comment: 15 pages. To be submitted to Proc. Am. Math. Soc
Externí odkaz:
http://arxiv.org/abs/2209.11598
Autor:
Pakhomov, Fedor, Zapryagaev, Alexander
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 self-interpretations are definably isomorphic to the trivial one. Here w
Externí odkaz:
http://arxiv.org/abs/2004.03404
Autor:
Zapryagaev, Alexander
Presburger Arithmetic $\mathop{\mathbf{PrA}}\nolimits$ is the true theory of natural numbers with addition. We consider linear orderings interpretable in Presburger Arithmetic and establish various necessary and sufficient conditions for interpretabi
Externí odkaz:
http://arxiv.org/abs/1911.07182
Autor:
Zapryagaev, Alexander, Pakhomov, Fedor
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 definably isomorphic to the identity self-interpretation. In order to
Externí odkaz:
http://arxiv.org/abs/1709.07341