论某些乌纳尔子集理论的不可判定性

IF 0.5 4区数学 Q3 MATHEMATICS

Doklady Mathematics Pub Date : 2024-04-18 DOI:10.1134/S1064562424701874

B. N. Karlov

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引用次数: 0

摘要

摘要本文致力于研究具有注入函数的单变量的算法特性。我们证明，如果语言是由可数的谓词符号集扩展的，那么每一个这样的unar的理论都允许量词消去。我们建立了量词消去有效的必要条件和充分条件，并提出了此类 Unar 理论的可解性准则。利用这个标准，我们建立了一个unar，使得它的理论是可判定的，但它的子集的unar理论是不可判定的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On Undecidability of Subset Theories of Some Unars

This paper is dedicated to studying the algorithmic properties of unars with an injective function. We prove that the theory of every such unar admits quantifier elimination if the language is extended by a countable set of predicate symbols. Necessary and sufficient conditions are established for the quantifier elimination to be effective, and a criterion for decidability of theories of such unars is formulated. Using this criterion, we build a unar such that its theory is decidable, but the theory of the unar of its subsets is undecidable.

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来源期刊

Doklady Mathematics 数学-数学

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

3-6 weeks

期刊介绍： Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.