Amalgamation, congruence-extension, and interpolation properties in algebras

DOI10.1007/BF02944991zbMath0236.02047MaRDI QIDQ2552131

Don Pigozzi

Publication date: 1972

Published in: Algebra Universalis (Search for Journal in Brave)

Mathematics Subject Classification ID

Structure theory of algebraic structures (08A05) Cylindric and polyadic algebras; relation algebras (03G15) Interpolation, preservation, definability (03C40)

Related Items (40)

Sentential logics and Maehara interpolation property ⋮ Bjarni Jónsson's contributions in algebra ⋮ Uniform interpolation and compact congruences ⋮ Geometry of Robinson consistency in Łukasiewicz logic ⋮ Modularity results for interpolation, amalgamation and superamalgamation ⋮ A note on neat reducts ⋮ Algebraic Characterization of the Local Craig Interpolation Property ⋮ Epimorphisms in varieties of residuated structures ⋮ Varying interpolation and amalgamation in polyadic MV-algebras ⋮ A Mathematical Life ⋮ Living without Beth and Craig: Definitions and Interpolants in Description and Modal Logics with Nominals and Role Inclusions ⋮ The Modelwise Interpolation Property of Semantic Logics ⋮ On deductive interpolation for the weak nilpotent minimum logic ⋮ Varieties of algebras with equationally definable zeros ⋮ New perspectives in algebraic logic, from neat embeddings to Erdős graphs ⋮ Galois Theory for Cylindric Algebras and its Applications ⋮ Interpolation and amalgamation in modal cylindric algebras ⋮ Uniform interpolation and coherence ⋮ Amalgamation and interpolation in normal modal logics ⋮ TWO-VARIABLE LOGIC HAS WEAK, BUT NOT STRONG, BETH DEFINABILITY ⋮ Neat embeddings as adjoint situations ⋮ Amalgamation and interpolation in ordered algebras. ⋮ Characterizing Mal'cev conditions ⋮ Neat embeddings, omitting types, and interpolation: an overview ⋮ Amalgamation properties and interpolation theorems for equational theories ⋮ Base-undecidable properties of universal varieties ⋮ Some results about neat reducts ⋮ Strong Amalgamation in Systems of Varieties ⋮ Craig's theorem in superintuitionistic logics and amalgamable varieties of pseudo-Boolean algebras ⋮ Amalgamation, interpolation, and implicit definability in varieties of algebras ⋮ Algebraic Logic, Where Does it Stand Today? ⋮ Modal languages and bounded fragments of predicate logic ⋮ The Robinson property and amalgamations of higher arities ⋮ On neat embeddings of cylindric algebras ⋮ Epimorphisms in cylindric algebras and definability in finite variable logic ⋮ Logical matrices and the amalgamation property ⋮ Modal logics and varieties of modal algebras: The Beth properties, interpolation, and amalgamation ⋮ Craig interpolation for semilinear substructural logics ⋮ Amalgamation properties in the class of MS-algebras ⋮ On amalgamation in algebras of logic

Cites Work

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• On the representation theory for cylindric algebras
• Universal homogeneous Boolean algebras
• Freedom in polyadic algebras and two theorems of Beth and Craig
• Classes without the amalgamation property
• Three uses of the Herbrand-Gentzen theorem in relating model theory and proof theory
• Linear reasoning. A new form of the Herbrand-Gentzen theorem
• Sublattices of a Free Lattice
• Dependence in groups
• On Automorphisms of Polyadic Algebras
• On a new notion of independence in universal algebras
• An extension of the Craig-Lyndon interpolation theorem
• The Structure of Pseudocomplemented Distributive Lattices. II: Congruence Extension and Amalgamation
• Products of abstract algebras

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