A SENTENCE PRESERVATION THEOREM FOR BOOLEAN ALGEBRAS

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 thi...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2023-04, Vol.271 (6), p.700-707
Main Author: Gutman, Alexander E.
Format: Article
Language:English
Subjects:
Algebra
Laws, regulations and rules
Mathematics
Mathematics and Statistics
Questions
Theorems
Venn diagrams
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Summary: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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-023-06599-4