A Set of Independent Axioms for Boolean Algebra
نویسنده
چکیده
1. Introduction IT is well known that there are a number of sets of axioms for Boolean algebra. In this paper, I give a set of five independent axioms using conditioned disjunction as the ternary operation which is postulated. The ternary operation is most naturally defined on the set 2 n —this is done in §2. The theorem is stated in §3 together with a slight generalization of this result; the existence of a unit element is omitted and the result is a set of axioms for a 'locally' Boolean algebra. A generalization of Stone's representation theorem for Boolean algebras is given in § 10. This deals with the representation of semi-lattices as subsets of a set. Finally, this result is used to give an alternative proof of my first theorem.
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