Ideals in a Polyadic Algebra1
نویسنده
چکیده
In an important sequence of papers, Halmos has developed the beautiful and significant theory of algebraic logic. The central mathematical object of this theory is the polyadic algebra, which incorporates in an axiomatic way the concepts of substitution, transformation, and quantification for the lower functional calculus. The beauty of the theory is revealed by the fact that the semantic completeness theorem of Godel becomes the algebraic theorem that every polyadic algebra is semisimple. The proof of semisimplicity is quite easy. The problem is reduced to proving that a monadic algebra is semisimple, and this in turn is reduced to Stone's theorem that any Boolean algebra is semisimple. The purpose of this note is to observe that this proof can be made to yield more information concerning the polyadic ideals of a polyadic algebra.
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