由正弦扩展的普雷斯伯格算术的可判定性边界

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2024-06-12 DOI:10.1016/j.apal.2024.103487

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引用次数: 0

摘要

我们考虑了由正弦函数扩展的普雷斯伯格算术，称这种扩展为正弦-普雷斯伯格算术（），并系统地研究了.PA 中句子集的判定问题。特别是，我们详细介绍了在沙努埃尔猜想的假设下存在的正弦-PA 句子的判定算法。这一过程将判定问题简化为由正弦扩展的实数有序加法群理论，而该理论在沙努埃尔猜想下是可判定的。另一方面，我们证明了四个交替量词块足以导致 sin-PA 句子的不可判定性。为此，我们明确地解释了网格的弱一元二阶理论，该理论在.NET 中是不可判定的。

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Decidability bounds for Presburger arithmetic extended by sine

We consider Presburger arithmetic extended by the sine function, call this extension sine-Presburger arithmetic (sin-PA), and systematically study decision problems for sets of sentences in sin-PA. In particular, we detail a decision algorithm for existential sin-PA sentences under assumption of Schanuel's conjecture. This procedure reduces decisions to the theory of the ordered additive group of real numbers extended by sine, which is decidable under Schanuel's conjecture. On the other hand, we prove that four alternating quantifier blocks suffice for undecidability of sin-PA sentences. To do so, we explicitly interpret the weak monadic second-order theory of the grid, which is undecidable, in sin-PA.

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来源期刊

Annals of Pure and Applied Logic 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

200 days

期刊介绍： The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.