On Two Ways of Representation of Uncountable Structures

IF 0.4 3区数学 Q4 LOGIC

Algebra and Logic Pub Date : 2026-07-30 DOI:10.1007/s10469-026-09838-0

A. S. Morozov

引用次数: 0

Abstract

An embedding of the hereditarily finite superstructure over the ordered field of real numbers into the set of reals is constructed which takes Σ-subsets to sets computable by infinite time Blum-Shub-Smale machines (ITBMs). A notion of ITBM-constructivizable structure is introduced. It is proved that constructivizability of an arbitrary algebraic structure over the ordered field of real numbers implies its ITBM-constructivizability. We obtain a theorem on the existence of ITBM-constructivizable models of the cardinality of the continuum for countable consistent theories with infinite models.

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论不可数结构的两种表示方式

构造了实数有序域上的遗传有限上结构嵌入到实数集合中，该集合取Σ-subsets到无限时间Blum-Shub-Smale机器（itbm）可计算的集合。引入了itbm可构造结构的概念。证明了实数有序域上任意代数结构的可构造性暗示了其itbm -可构造性。对于具有无限模型的可数相容理论，我们得到了连续统基数的itbm可构造模型的存在性定理。

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.