A Sequence of Models of Generalized Second-order Dedekind Theory of Real Numbers with Increasing Powers

Zakharov, Valeriy K. and Rodionov, Timofey V. (2020) A Sequence of Models of Generalized Second-order Dedekind Theory of Real Numbers with Increasing Powers. Asian Research Journal of Mathematics, 16 (1). pp. 13-39. ISSN 2456-477X

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Abstract

The paper is devoted to construction of some closed inductive sequence of models of the generalized second-order Dedekind theory of real numbers with exponentially increasing powers. These models are not isomorphic whereas all models of the standard second-order Dedekind theory are. The main idea in passing to generalized models is to consider instead of superstructures with the single common set-theoretical equality and the single common set-theoretical belonging superstructures with several generalized equalities and several generalized belongings for rst and second orders. The basic tools for the presented construction are the infraproduct of collection of mathematical systems different from the factorized Los ultraproduct and the corresponding generalized infrafiltration theorem. As its auxiliary corollary we obtain the generalized compactness theorem for the generalized second-order language.

Item Type: Article
Subjects: STM Open Press > Mathematical Science
Depositing User: Unnamed user with email support@stmopenpress.com
Date Deposited: 03 Mar 2023 09:16
Last Modified: 31 Jul 2024 12:57
URI: http://journal.submissionpages.com/id/eprint/524

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