A Theory of Boolean Valued Functions and Partitions
نویسندگان
چکیده
In this paper Y denotes a non empty set. Let k, l be elements of Boolean. The functor k ⇒ l is defined by: (Def. 1) k ⇒ l = ¬k ∨ l. The functor k ⇔ l is defined as follows: (Def. 2) k ⇔ l = ¬(k ⊕ l). Let k, l be elements of Boolean. The predicate k ⋐ l is defined by: (Def. 3) k ⇒ l = true. Let us note that the predicate k ⋐ l is reflexive. One can prove the following three propositions: (1) For all elements k, l of Boolean and for all natural numbers n1, n2 such that k = n1 and l = n2 holds k ⋐ l iff n1 ¬ n2.
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