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A sentence preservation theorem for Boolean algebras Full article

Journal Journal of Mathematical Sciences (United States)
ISSN: 1072-3374 , E-ISSN: 1573-8795
Output data Year: 2023, Volume: 271, Number: 6, Pages: 700-707 Pages count : 8 DOI: 10.1007/s10958-023-06599-4
Tags Boolean algebra, Venn diagram, truth table, Horn formula
Authors Gutman A.E. 1,2
Affiliations
1 Sobolev Institute of Mathematics
2 Novosibirsk State University

Funding (1)

1 Sobolev Institute of Mathematics FWNF-2022-0004

Abstract: At the initial stages of studying the theory of Boolean algebras, before trying to prove or disprove any simple sentence, students are usually asked to test their intuition using Venn diagrams or truth tables. A natural question arises: is it necessary to invent a proof after a positive check of this kind? Isn't such a check itself a rigorous proof of the verified sentence? And if this is not true in the general case, for which sentences is this true? We answer the question and prove an analog of the Jech Theorem for arbitrary (not necessarily complete) Boolean algebras.
Cite: Gutman A.E.
A sentence preservation theorem for Boolean algebras
Journal of Mathematical Sciences (United States). 2023. V.271. N6. P.700-707. DOI: 10.1007/s10958-023-06599-4 Scopus РИНЦ OpenAlex
Dates:
Accepted: Jul 31, 2023
Published print: Oct 27, 2023
Published online: Oct 27, 2023
Identifiers:
Scopus: 2-s2.0-85174826319
Elibrary: 63486767
OpenAlex: W4388194954
Citing: Пока нет цитирований
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