Order, lattices, ordered algebraic structures Boolean algebras Concept
Boolean algebra
Summary
A Boolean algebra is a structure with meet, join and complement that satisfies the laws of classical logic and of set algebra. It is the algebra of propositional logic and of digital circuits. The node Boolean algebra gives the precise definition.
Where this leads
21 pages build on this one.
- Atomless Boolean algebra
- Ultrafilter lemma
- Boolean-valued model
- Stone duality
- Heyting algebra
- Algebraic logic
- Free Boolean algebra
- Ultrafilter on a Boolean algebra
- Measure algebra
- Lindenbaum–Tarski algebra
- Equivalence of Boolean rings and Boolean algebras
- MV-algebra
- Relation algebra
- Cylindric algebra
- Stone's representation theorem for Boolean algebras
- Residuated lattice
- Foster's theorem on primal algebras
- Complete Boolean algebra
- Huntington's axioms
- Robbins conjecture
- Isomorphism theorem for measure algebras
Further reading
About this page
| Tag | 0XADJKM699 |
|---|---|
| URI | m2://0XADJKM699 |
| Kind | concept |
| Writing | W1 stated |
| MSC | 06E05 |
| Same as |
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What this page needs for W2
- edge not_instance_of in: at least one non-example (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Instances
Definitions
Special cases
- Cylindric algebra
- Free Boolean algebra
- Complete Boolean algebra
- Interior algebra
- Relation algebra
- Atomless Boolean algebra
- Measure algebra
Used by
- Atomless Boolean algebra
- Ultrafilter lemma
- Boolean-valued model
- Stone duality
- Heyting algebra
- Algebraic logic
- Free Boolean algebra
- Ultrafilter on a Boolean algebra
- Measure algebra
- Lindenbaum–Tarski algebra
- Equivalence of Boolean rings and Boolean algebras
- MV-algebra
- Relation algebra
- Cylindric algebra
- Stone's representation theorem for Boolean algebras
- Foster's theorem on primal algebras
- Complete Boolean algebra
- Huntington's axioms
- Robbins conjecture
- Isomorphism theorem for measure algebras