Index Sets of Decidably Categorical Models that are Elementarily Equivalent to the Powers of Omega

IF 0.4 3区数学 Q4 LOGIC

Algebra and Logic Pub Date : 2026-08-27 DOI:10.1007/s10469-026-09842-4

N. A. Bazhenov, M. V. Zubkov, M. I. Marchuk

引用次数: 0

Abstract

A strongly constructivizable model S is decidably categorical if for any decidable copies A and B of S, there exists a computable isomorphism from A onto B. The paper investigates the complexity of families of decidably categorical models belonging to familiar finitely axiomatizable classes. For a non-zero natural number n, the index set of decidably categorical linear orders elementarily equivalent to the ordinal ωⁿ is an m-complete \({\Sigma}_{2\text{n}+2}^{0}\)-set. The index set of decidably categorical structures which are elementarily equivalent to ωⁿ, enriched by the successor relation, is an m-complete \({\Sigma}_{2\text{n}+1}^{0}\)-set.

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基本等价于的幂的可确定范畴模型的索引集

如果对于S的任意可决副本A和B，存在A到B的可计算同构，则强可构造模型S是可决范畴的。本文研究了属于有限公化类的可决范畴模型族的复杂性。对于非零自然数n，与序数ωn初等等价的定范畴线性阶的指标集是一个m完全\({\Sigma}_{2\text{n}+2}^{0}\) -集。初等等价于ωn的确定范畴结构的指标集，由后继关系充实，是一个m完全\({\Sigma}_{2\text{n}+1}^{0}\) -集。

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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来源期刊

Algebra and Logic 数学-数学

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

>12 weeks

期刊介绍： This bimonthly journal publishes results of the latest research in the areas of modern general algebra and of logic considered primarily from an algebraic viewpoint. The algebraic papers, constituting the major part of the contents, are concerned with studies in such fields as ordered, almost torsion-free, nilpotent, and metabelian groups; isomorphism rings; Lie algebras; Frattini subgroups; and clusters of algebras. In the area of logic, the periodical covers such topics as hierarchical sets, logical automata, and recursive functions. Algebra and Logic is a translation of ALGEBRA I LOGIKA, a publication of the Siberian Fund for Algebra and Logic and the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences. All articles are peer-reviewed.