Craig's theorem in superintuitionistic logics and amalgamable varieties of pseudo-Boolean algebras

DOI10.1007/BF01670006zbMath0413.03018MaRDI QIDQ1260029

Larisa L. Maksimova

Publication date: 1978

Published in: Algebra and Logic (Search for Journal in Brave)

zbMATH Keywords

decision problemsuperintuitionistic logicsCraig's interpolation theoremamalgamable varieties of pseudo-Boolean algebras

Mathematics Subject Classification ID

Logical aspects of lattices and related structures (03G10) Intuitionistic mathematics (03F55) Intermediate logics (03B55)

Related Items (39)

Hybrid extensions of the minimal logic ⋮ Extensions of the minimal logic and the interpolation problem ⋮ Layers over minimal logic ⋮ Uniform Lyndon interpolation for basic non-normal modal logics ⋮ Nonmodular lattices derived from distributive ones representing qualitative biologic interactions ⋮ The algebraic relational theory in the analysis of the reversibility of biological processes becoming malignant ⋮ Lattices due to increasing low energy relational processes ⋮ On the interpolation property of some intuitionistic modal logics ⋮ On extensions of intermediate logics by strong negation ⋮ Changing algebras in low energy biologic relational processes ⋮ Recognizable logics ⋮ The small index property of the Fraïssé limit of finite Heyting algebras ⋮ THE AUTOMORPHISM GROUP OF THE FRAÏSSÉ LIMIT OF FINITE HEYTING ALGEBRAS ⋮ The decidability of Craig's interpolation property in well-composed J-logics ⋮ First-order interpolation derived from propositional interpolation ⋮ Craig's interpolation property in pretabular logics ⋮ Restricted interpolation property in superintuitionistic logics ⋮ Decidability of the interpolation problem and of related properties in tabular logics ⋮ Complemented MacNeille completions and algebras of fractions ⋮ Interpolation and definability over the logic Gl ⋮ Fatal Heyting algebras and forcing persistent sentences ⋮ On classical behavior of intuitionistic modalities ⋮ The lattice of Belnapian modal logics: Special extensions and counterparts ⋮ The Lyndon property and uniform interpolation over the Grzegorczyk logic ⋮ Epimorphisms in varieties of subidempotent residuated structures ⋮ The disjunction property of intermediate propositional logics ⋮ Interpolation over the minimal logic and Odintsov intervals ⋮ Recognizable and perceptible logics and varieties ⋮ Interpolation and the projective Beth property in well-composed logics ⋮ Decidability of the weak interpolation property over the minimal logic ⋮ Undecidability of the problem of recognizing axiomatizations of superintuitionistic propositional calculi ⋮ Reactive intuitionistic tableaux ⋮ The interpolation problem in finite-layered pre-Heyting logics ⋮ Definability and interpolation in non-classical logics ⋮ Bounded distributive lattices with strict implication ⋮ On Algebraisation of Superintuitionistic Predicate Logics ⋮ Amalgamation, interpolation, and implicit definability in varieties of algebras ⋮ On semiconic idempotent commutative residuated lattices ⋮ Constructive classifications of modal logics and extensions of minimal logic

Cites Work

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• Der Interpolationssatz der intuitionistischen Prädikatenlogik
• Amalgamation properties and interpolation theorems for equational theories
• Base-undecidable properties of universal varieties
• Amalgamation, congruence-extension, and interpolation properties in algebras
• The amalgamation property in equational classes of modular lattices
• Three uses of the Herbrand-Gentzen theorem in relating model theory and proof theory
• A propositional calculus with denumerable matrix
• The Structure of Pseudocomplemented Distributive Lattices. II: Congruence Extension and Amalgamation

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