Locally finite varieties of Heyting algebras
نویسندگان
چکیده
We show that for a variety V of Heyting algebras the following conditions are equivalent: (1) V is locally finite; (2) the V-coproduct of any two finite V-algebras is finite; (3) either V coincides with the variety of Boolean algebras or finite V-copowers of the three element chain 3 ∈ V are finite. We also show that a variety V of Heyting algebras is generated by its finite members if, and only if, V is generated by a locally finite V-algebra. Finally, to the two existing criteria for varieties of Heyting algebras to be finitely generated we add the following one: V is finitely generated if, and only if, V is residually finite.
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