Complete and independent sets of axioms of Boolean algebra

Abstract

We investigate fundamental properties of axioms of Boolean algebra in detail by using the method of indeterminate coefficients, which uses multiple-valued logic. We can prove that four axioms, one of the commutative laws, one of the complementary laws, one of the distributive laws and one of the least element(a), greatest element (b) and the absorption laws are independent from others in the set of fundamental axioms of Boolean algebra. Then we research candidates, including those four axioms and other smaller number of axioms and prove all of those candidates are indeed complete and independent sets of axioms of the algebra.