Decidable quasivarieties of p‐algebras

We show that for quasivarieties of p‐algebras the properties of (i) having decidable first‐order theory and (ii) having decidable first‐order theory of the finite members, coincide. The only two quasivarieties with these properties are the trivial variety and the variety of Boolean algebras. This co...

Full description

Saved in:
Bibliographic Details
Published inMathematical logic quarterly Vol. 71; no. 1
Main Authors Kowalski, Tomasz, Słomczyńska, Katarzyna
Format Journal Article
LanguageEnglish
Published Berlin Wiley Subscription Services, Inc 01.02.2025
Online AccessGet full text

Cover

More Information
Summary:We show that for quasivarieties of p‐algebras the properties of (i) having decidable first‐order theory and (ii) having decidable first‐order theory of the finite members, coincide. The only two quasivarieties with these properties are the trivial variety and the variety of Boolean algebras. This contrasts sharply, even for varieties, with the situation in Heyting algebras where decidable varieties do not coincide with finitely decidable ones.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0942-5616
1521-3870
DOI:10.1002/malq.202300064