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Heyting algebra

In mathematics, a Heyting algebra (also known as pseudo-Boolean algebra) is a bounded lattice (with join and meet operations written ∨ and ∧ and with least element 0 and greatest element 1) equipped with a binary operation a → b called implication such that (c ∧ a) ≤ b is equivalent to c ≤ (a → b). In a Heyting algebra a ≤ b can be found to be equivalent…

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Formal definition

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Properties

Quotients

Universal constructions

Heyting algebras as applied to intuitionistic logic

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Topological representation and duality theory

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Heyting algebra

Nodes92
Edges91
Triples194
Avg. degree1.98
Density0.021739
Components1

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Heyting algebra

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related to References · 57
Heyting algebra → Acad, Applications, Berlin, Borceux, Boyd, Cambridge, Cambridge University Press, Canada XVI, Categorical Algebra, Continuous Lattices, Daniel Edwin, Dickmann, Die, Domains, Free Heyting, Geometry, Ghilardi, Gierz, Handbook, Heyting
related to Heyting algebra of propositional formulas in n variables up to intuitionist equivalence · 22
Heyting algebra → A1, A2, An, Consider, Endow, EQUIV, FALSE, Finally, Further, H0, Heyting, In, It, Let H0, MODUS-PONENS, Operations, Provable, The, THEN-1, This
related to Examples · 20
Heyting algebra → Ac, Boolean, Every, Every Boolean, Every Heyting, For, Given, H1, Heyting, Hreg, In, LMn, Moisil, More, MV-algebras, Not, The, The Lindenbaum, These, This
related to Comparison to Lindenbaum algebras · 10
Heyting algebra → Ai, Boolean, BT, Heyting, HT, In, Lindenbaum, T1, The, The Lindenbaum
related to Decision problems · 10
Heyting algebra → Boolean, Heyting, Horn, It, PSPACE-complete, Regarding, Richard Statman, Saul Kripke, Stephen Cook, The
related to Heyting algebra of formulas equivalent with respect to a theory T · 10
Heyting algebra → Ai, Given, H0, Heyting, HT, Let, Provable, The, The Heyting, Then HT
related to Characterization using the axioms of intuitionistic logic · 9
Heyting algebra → Compare, For, Given, Heyting, Intuitionistic, One, Provable, This, Universal
related to Free Heyting algebra on an arbitrary set of generators · 8
Heyting algebra → Ai, H0, Heyting, In, It, One, Provable, The
related to Heyting algebras as applied to intuitionistic logic · 6
Heyting algebra → But, For, Furthermore, Heyting, If, This
related to Topological representation and duality theory · 5
Heyting algebra → Every Heyting, Heyting, More, Stone, This

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heyting algebra algebras displaystyle elements set boolean lattice element logic definition given every law true follows form distributive morphism formulas

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SubjectPredicateObjectConfidenceSrc
Heyting algebrais aHeyting algebra that is a complete lattice.A subalgebra of a Heyting algebra H is a subset H1 of H containing 0 and 1 and closed under the operations0.90text
Heyting algebrais atrivial one-element Heyting algebra.Provable identitiesGiven a formula F0.90text
Heyting algebrais atrivial one-element Heyting algebra0.90text
Heyting algebrarelated to Bounded lattice with an implication operationGiven0.60section
Heyting algebrarelated to Bounded lattice with an implication operationHeyting0.60section
Heyting algebrarelated to Category-theoretic definitionHeyting0.60section
Heyting algebrarelated to Category-theoretic definitionThe0.60section
Heyting algebrarelated to Characterization using the axioms of intuitionistic logicThis0.60section
Heyting algebrarelated to Characterization using the axioms of intuitionistic logicHeyting0.60section
Heyting algebrarelated to Characterization using the axioms of intuitionistic logicFor0.60section
Heyting algebrarelated to Characterization using the axioms of intuitionistic logicProvable0.60section
Heyting algebrarelated to Characterization using the axioms of intuitionistic logicUniversal0.60section

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