Amalgamation and interpolation in the category of Heyting algebras

DOI10.1016/0022-4049(83)90104-4zbMath0517.18004OpenAlexW2001916998MaRDI QIDQ1053098

Andrew M. Pitts

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1016/0022-4049(83)90104-4

zbMATH Keywords

category of framesintuitionistic propositional logiccategory of distributive latticescategorical formulations of Beth definability theoremcategorical formulations of Craig interpolation theoremcategory of Heyting algebras and homomorphismscategory of locales and open mapsGalois theory of Grothendiecklattice of filters in a latticestability of monomorphisms under pushout

Mathematics Subject Classification ID

Logical aspects of lattices and related structures (03G10) Heyting algebras (lattice-theoretic aspects) (06D20) Lattice ideals, congruence relations (06B10) Categories admitting limits (complete categories), functors preserving limits, completions (18A35) Products, amalgamated products, and other kinds of limits and colimits (08B25) Interpolation, preservation, definability (03C40) Foundations, relations to logic and deductive systems (18A15)

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Cites Work

• An application of open maps to categorical logic
• Completeness results for intuitionistic and modal logic in a categorical setting
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