On Two Ways of Representation of Uncountable Structures

On Two Ways of Representation of Uncountable Structures Full article

Journal

Algebra and Logic
ISSN: 0002-5232 , E-ISSN: 1573-8302

Output data

Year: 2026, Volume: 64, Number: 5, Pages: 330-348 Pages count : 19 DOI: 10.1007/s10469-026-09838-0

Tags

infinite time Blum-Shub-Smale machines, ITBM-constructivizable structure, hereditarily finite superstructure, algebraic structure, ordered field of real numbers

Authors

Morozov A.S. ^1,2

Affiliations

1	Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences
2	Novosibirsk State University, Novosibirsk

Funding (1)

Russian Science Foundation

23-11-00170

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.

Morozov A.S.
On Two Ways of Representation of Uncountable Structures
Algebra and Logic. 2026. V.64. N5. P.330-348. DOI: 10.1007/s10469-026-09838-0 WOS OpenAlex

≡ Web of science:	WOS:001836148400001
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