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On some connections between Boolean algebras and Heyting algebras. (English) Zbl 0779.06010
Summary: We present a finitely axiomatizable class of Heyting algebras (with identity \((-x)+(--x)=1\)) such that this class and the class of Boolean algebras with \(n\) distinguished ideals are mutually first-order definable. As a corollary some results on countable categoricity, finite axiomatizability, decidability, prime and countably saturated models for Heyting algebras are obtained.
MSC:
06E99 Boolean algebras (Boolean rings)
06D20 Heyting algebras (lattice-theoretic aspects)
03C07 Basic properties of first-order languages and structures
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