A complemented distributive lattice on a two-element set {0, 1} with meet (∧), join (∨), and complement (¬). Equivalent (as an algebraic structure) to propositional logic under the identification 0↔F, 1↔T, ∧↔AND, ∨↔OR, ¬↔NOT. The…
Boolean algebra
Related concepts
- Logical conjunction (AND)
- Logical disjunction (OR)
- Logical negation (NOT)
- Dilworth: width(P) = min chain cover
- Birkhoff HSP theorem: variety = class closed under H, S, P
- Con(A) is a complete algebraic lattice; Mal'tsev conditions
- Open mapping + closed graph
- Kolmogorov complexity + MDL
- Tarski semantic truth
- Compactness theorem (Gödel)
- NIP theory (Shelah)
- Definable sets + quantifier elimination
- Hilbert program + finitism
- Gentzen sequent calculus + cut-elimination
- Intuitionistic logic (Heyting)
- Modal logic + Kripke frames
- Realisability (Kreisel-Kleene)
- Turing machine + halting problem
- Post correspondence problem
- Kolmogorov complexity (cross)