free Boolean algebra
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(algebra) 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 22ⁿ 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.
free Boolean algebra
A free Boolean algebra generated by n independent generators has 22n elements, each corresponding to a Boolean formula determined by the valuations of those generators.
A free Boolean algebra generated by n independent generators has 22n elements, each corresponding to a Boolean formula determined by the valuations of those generators.
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