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Finitely axiomatizable Boolean algebras with distinguished ideals. (Russian) Zbl 0647.03026
For any natural number m, \({\mathcal B}_ m\) denotes the class of Boolean algebras with m distinguished ideals. The main results of the reviewed paper are the following: 1) a description of those \(B\in {\mathcal B}_ m\) for which Th(B) are finitely axiomatizable; 2) a proof that \(B\in {\mathcal B}_ m\) is local in the sense of the author [Countable-categorical Boolean algebras with distinguished ideals, Preprint (1986)] iff B is a direct summand of a B’\(\in {\mathcal B}_ m\) for which Th(B) is finitely axiomatizable; 3) a semantical characterization of the elementary equivalence for systems from \({\mathcal B}_ m\) and characterization of the systems \(B\in {\mathcal B}_ m\) for which Th(B) are decidable; 4) a proof that Th(\({\mathcal B}_ m)\) are decidable (this generalizes the theorem of M. Rabin [Trans. Am. Math. Soc. 141, 1-35 (1969; Zbl 0221.02031)] on decidability of Th(\({\mathcal B}_ 1))\); 5) a proof that any sentence (of the language corresponding to \({\mathcal B}_ m)\) which is consistent with Th(\({\mathcal B}_ m)\) has in \({\mathcal B}_ m\) a finitely axiomatizable model and a strong constructivizable model.
Reviewer: S.R.Kogalovskij

03C35 Categoricity and completeness of theories
06E99 Boolean algebras (Boolean rings)
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