Atom structures of cylindric algebras and relation algebras

DOI10.1016/S0168-0072(97)00015-8zbMath0898.03025OpenAlexW2120627125MaRDI QIDQ1377624

I. M. Hodkinson

Publication date: 1 November 1998

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0168-0072(97)00015-8

zbMATH Keywords

representabilitycompletionrelation algebrasaxiomatizabilitycylindric algebras

Mathematics Subject Classification ID

Equational classes, universal algebra in model theory (03C05) Cylindric and polyadic algebras; relation algebras (03G15)

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Cites Work

• Unnamed Item
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• Some kinds of modal completeness
• Atom structures and Sahlqvist equations
• Complexity of equations valid in algebras of relations. II: Finite axiomatizations
• Elementary generation and canonicity for varieties of Boolean algebras with operators
• Relation algebras with \(n\)-dimensional relational bases
• On representable relation algebras
• Representations of integral relation algebras
• The representation of relational algebras
• Representability is not decidable for finite relation algebras
• Some Varieties Containing Relation Algebras
• On Moschovakis closure ordinals
• Step by step – Building representations in algebraic logic
• Complete representations in algebraic logic
• Nonfinitizability of classes of representable cylindric algebras
• Completions of B<scp>OOLEAN</scp> Algebras with operators
• The Theory of Representation for Boolean Algebras
• Boolean Algebras with Operators