Locally finite varieties of Heyting algebras

We show that for a variety of Heyting algebras the following conditions are equivalent: (1) is locally finite; (2) the -coproduct of any two finite -algebras is finite; (3) either coincides with the variety of Boolean algebras or finite -copowers of the three element chain are finite. We also show t...

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Bibliographic Details
Published in:Algebra universalis 2005-12, Vol.54 (4), p.465-473
Main Authors: Bezhanishvili, Guram, Grigolia, Revaz
Format: Article
Language:English
Subjects:
Boolean algebra
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Summary:We show that for a variety of Heyting algebras the following conditions are equivalent: (1) is locally finite; (2) the -coproduct of any two finite -algebras is finite; (3) either coincides with the variety of Boolean algebras or finite -copowers of the three element chain are finite. We also show that a variety of Heyting algebras is generated by its finite members if, and only if, is generated by a locally finite -algebra. Finally, to the two existing criteria for varieties of Heyting algebras to be finitely generated we add the following one: is finitely generated if, and only if, is residually finite.
ISSN:0002-5240
1420-8911
DOI:10.1007/s00012-005-1958-5