TY - JOUR

T1 - A sentence preservation theorem for Boolean algebras

AU - Гутман, Александр Ефимович

N1 - The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF-2022-0004).

PY - 2023/4

Y1 - 2023/4

N2 - 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.

AB - 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.

KW - Boolean algebra

KW - Horn formula

KW - Venn diagram

KW - truth table

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85174826319&origin=inward&txGid=1adf4e9716373870307f35ef9561fcd3

UR - https://www.mendeley.com/catalogue/a7d7d979-b658-3f64-97af-8db523fcf61e/

U2 - 10.1007/s10958-023-06599-4

DO - 10.1007/s10958-023-06599-4

M3 - Article

VL - 271

SP - 700

EP - 707

JO - Journal of Mathematical Sciences (United States)

JF - Journal of Mathematical Sciences (United States)

SN - 1072-3374

IS - 6

ER -