free Boolean algebra
free Boolean algebra noun: a field of sets whose elements are equivalent to Boolean formulas (or, perhaps more precisely, equivalence classes of Boolean formulas). Starting with a set of n variables which are independent of each other and are called generators, the power set of this set has 2ⁿmembers which may be called atoms and are valuations of the n variables: a valuation can be considered to be a set of variables which are "true" under that valuation, or a conjunction of generators (such that variables not included in that set are included in negated form in the equivalent conjunction). Then the power set of the set of atoms yields a set of 2^(2ⁿ) members which are the elements of the said field of sets. These elements correspond to Boolean formulas: a formula can be considered to be a set of valuations which make the formula true, or a linear combination (i.e., a disjunction) of atoms.
Noun
free Boolean algebra (plural free Boolean algebras)
- A field of sets whose elements are equivalent to Boolean formulas (or, perhaps more precisely, equivalence classes of Boolean formulas). Starting with a set of n variables which are independent of each other and are called generators, the power set of this set has 2ⁿmembers which may be called atoms and are valuations of the n variables: a valuation can be considered to be a set of variables which are "true" under that valuation, or a conjunction of generators (such that variables not included in that set are included in negated form in the equivalent conjunction). Then the power set of the set of atoms yields a set of 2^(2ⁿ) members which are the elements of the said field of sets. These elements correspond to Boolean formulas: a formula can be considered to be a set of valuations which make the formula true, or a linear combination (i.e., a disjunction) of atoms.
Forms of free Boolean algebra
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Questions about free Boolean algebra
- What does free Boolean algebra mean?
- Free Boolean algebra means a field of sets whose elements are equivalent to Boolean formulas (or, perhaps more precisely, equivalence classes of Boolean formulas). Starting with a set of n variables which are independent of each other and are called generators, the power set of this set has 2ⁿmembers which may be called atoms and are valuations of the n variables: a valuation can be considered to be a set of variables which are "true" under that valuation, or a conjunction of generators (such that variables not included in that set are included in negated form in the equivalent conjunction). Then the power set of the set of atoms yields a set of 2^(2ⁿ) members which are the elements of the said field of sets. These elements correspond to Boolean formulas: a formula can be considered to be a set of valuations which make the formula true, or a linear combination (i.e., a disjunction) of atoms.
- What part of speech is free Boolean algebra?
- Free Boolean algebra is a noun.
- What is the plural of free Boolean algebra?
- The plural of free Boolean algebra is free Boolean algebras.
Words near free Boolean algebra in the dictionary
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Adapted from Wiktionary: free Boolean algebra (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.
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