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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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##### References:
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