Applications of a theorem of Lévy to Boolean terms and algebras

Author:
Jonathan Stavi

Journal:
Trans. Amer. Math. Soc. **205** (1975), 1-36

MSC:
Primary 02B25; Secondary 02J05, 02K30

MathSciNet review:
0469695

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Abstract: The paper begins with a short proof of the Gaifman-Hales theorem and the solution of a problem of Gaifman about the depth and length of Boolean terms. The main results are refinements of the following theorem: Let be regular, . A -complete Boolean algebra on generators, which are restricted by just one countably long equation, is either atomic with atoms or isomorphic to the free -complete Boolean algebra on generators. The main tools are a Skolem-Löwenheim type theorem of Azriel Lévy and a coding of Borel sets and Borel-measurable functions by Boolean terms.

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DOI:
https://doi.org/10.1090/S0002-9947-1975-0469695-0

Article copyright:
© Copyright 1975
American Mathematical Society