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5) a^ß-^ß^a. (Vn)[ß(n)^a(n)]-+ ß^a. Since by (3) the behavior of finite sets is as trivially expected we shall be concerned primarily with infinite sets and thus (4) will be applicable. is a reflexive and transitive relation, hence by partially ordered set theory, if a~ß is defined as "a^ß and ß}ta", then ~ is an equivalence relation and thedoi:10.1090/s0002-9947-1969-0239973-6 fatcat:my3sypoyuvezze6kdxyppdhzdu