Axiomatizability of reducts of algebras of relations | Zendy

Ian Hodkinson | Zendy; Szabolcs Mikul�s | Zendy

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Axiomatizability of reducts of algebras of relations

Author(s) -

Ian Hodkinson,

Szabolcs Mikul�s

Publication year - 2000

Publication title -

algebra universalis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.516

H-Index - 31

eISSN - 1420-8911

pISSN - 0002-5240

DOI - 10.1007/s000120050150

Subject(s) - mathematics , converse , intersection (aeronautics) , class (philosophy) , relation (database) , similarity (geometry) , pure mathematics , characterization (materials science) , type (biology) , algebra over a field , computer science , image (mathematics) , ecology , materials science , geometry , database , artificial intelligence , engineering , nanotechnology , biology , aerospace engineering

. In this paper, we prove that any subreduct of the class of representable relation algebras whose similarity type includes intersection, relation composition and converse is a non-finitely axiomatizable quasivariety and that its equational theory is not finitely based. We show the same result for subreducts of the class of representable cylindric algebras of dimension at least three whose similarity types include intersection and cylindrifications. A similar result is proved for subreducts of the class of representable sequential algebras.

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