On the elementary equivalence of automorphism groups of Boolean algebras; downward Skolem Löwenheim theorems and compactness of related quantifiers

DOI10.2307/2273187zbMath0445.03012OpenAlexW1975559085MaRDI QIDQ3889028

Matatyahu Rubin, Saharon Shelah

Publication date: 1980

Published in: Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2273187

zbMATH Keywords

elementary equivalenceJensen's principleatomic Boolean algebrasparametric definabilityautomorphism groups of Boolean algebrasdyadic quantifierquantifier compactness

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Structure and representation theory of distributive lattices (06D05) Logic with extra quantifiers and operators (03C80) Nonstandard models of arithmetic (03H15) Automorphisms and endomorphisms of algebraic structures (08A35) Model theory of denumerable and separable structures (03C15) Infinite automorphism groups (20B27) Distributive lattices (06D99)

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Cites Work

• On the automorphism groups of homogeneous and saturated Boolean algebras
• First order theory of permutation groups
• On elementary types of symmetric groups
• Models with second order properties I. Boolean algebras with no definable automorphisms