Model completions and r-Heyting categories

DOI10.1016/S0168-0072(97)00012-2zbMath0888.03024MaRDI QIDQ1372155

Silvio Ghilardi, Marek W. Zawadowski

Publication date: 11 May 1998

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

zbMATH Keywords

varietiescategorical structureequational theoryintuitionistic propositional calculusmodel completion\(r\)-regular categorycategory of finitely represented Heyting algebrascategory of locally presented \(T\)-algebrasfirst-order theory of Heyting algebrasHeyting categoryquantifier-elemination

Mathematics Subject Classification ID

Categorical logic, topoi (03G30) Heyting algebras (lattice-theoretic aspects) (06D20) Boolean algebras with additional operations (diagonalizable algebras, etc.) (06E25) Categories of algebras (08C05) Axiomatic model classes (08C10) Models of other mathematical theories (03C65) Quantifier elimination, model completeness, and related topics (03C10)

Related Items (13)

Uniform interpolation and compact congruences ⋮ The small index property of the Fraïssé limit of finite Heyting algebras ⋮ THE AUTOMORPHISM GROUP OF THE FRAÏSSÉ LIMIT OF FINITE HEYTING ALGEBRAS ⋮ Model completion of scaled lattices and co‐Heyting algebras of p‐adic semi‐algebraic sets ⋮ Free Heyting algebra endomorphisms: Ruitenburg’s Theorem and beyond ⋮ Uniform interpolation and coherence ⋮ On Bellissima's construction of the finitely generated free Heyting algebras, and beyond ⋮ EXISTENTIALLY CLOSED BROUWERIAN SEMILATTICES ⋮ Fixed-Point Elimination in the Intuitionistic Propositional Calculus ⋮ Model completeness, uniform interpolants and superposition calculus. (With applications to verification of data-aware processes) ⋮ Combination of uniform interpolants via Beth definability ⋮ Combined covers and Beth definability ⋮ MODEL COMPLETIONS FOR UNIVERSAL CLASSES OF ALGEBRAS: NECESSARY AND SUFFICIENT CONDITIONS

Cites Work

• Unnamed Item
• Unnamed Item
• A finite basis theorem for quasivarieties
• Representation of categories
• Conceptual completeness for first-order intuitionistic logic: An application of categorical logic
• Varieties with equationally definable principal congruences
• Semantical investigations in Heyting's intuitionistic logic
• Model theory.
• Model-companions and definability in existentially complete structures
• Completeness results for intuitionistic and modal logic in a categorical setting
• On the structure of varieties with equationally definable principal congruences. I
• Lokal präsentierbare Kategorien. (Locally presentable categories)
• On an interpretation of second order quantification in first order intuitionistic propositional logic
• A sheaf representation and duality for finitely presented Heyting algebras

This page was built for publication: Model completions and r-Heyting categories