论文标题
前爆炸算术本身的多维解释本身
Multi-Dimensional Interpretations of Presburger Arithmetic in Itself
论文作者
论文摘要
Presburger算术是自然数的真实理论。我们本身研究了前爆发算术的解释。本文的主要结果是，所有自我解释绝对是琐碎的同构。在这里，我们考虑可能是多维的解释。我们注意到，这解决了A. Visser的猜想。为了证明结果，我们证明了所有可解释的线性顺序在$（\ Mathbb {n};+）$中都是有限的Hausdorff等级的分散订单，并且等级在相应解释的尺寸的术语中有限。
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 we consider interpretations that might be multi-dimensional. We note that this resolves a conjecture by A. Visser. In order to prove the result we show that all linear orderings that are interpretable in $(\mathbb{N};+)$ are scattered orderings with the finite Hausdorff rank and that the ranks are bounded in the terms of the dimensions of the respective interpretations.
