Predicate Calculus for Boolean Valued Functions. Part VIII
نویسنده
چکیده
The terminology and notation used here are introduced in the following articles: [1], [2], [3], [4], and [5]. In this paper Y is a non empty set. We now state a number of propositions: (1) For every element a of BVF(Y ) and for every subset G of PARTITIONS(Y ) and for all partitions A, B of Y holds ¬∃∀a,AG,BG ⋐ ∃∃ ¬a,BG,AG. (2) Let a be an element of BVF(Y ), G be a subset of PARTITIONS(Y ), and A, B, C be partitions of Y . Suppose G is a coordinate and G = {A, B,C} and A 6= B and B 6= C and C 6= A. Then ∃¬∀a,AG,BG ⋐ ∃∃¬a,BG,AG. (3) Let a be an element of BVF(Y ), G be a subset of PARTITIONS(Y ), and A, B, C be partitions of Y . Suppose G is a coordinate and G = {A, B,C} and A 6= B and B 6= C and C 6= A. Then ¬∀∀a,AG,BG ⋐ ∃¬∀a,BG,AG. (4) Let a be an element of BVF(Y ), G be a subset of PARTITIONS(Y ), and A, B, C be partitions of Y . Suppose G is a coordinate and G = {A, B,C} and A 6= B and B 6= C and C 6= A. Then ∀¬∀a,AG,BG ⋐ ∃∃¬a,BG,AG. (5) Let a be an element of BVF(Y ), G be a subset of PARTITIONS(Y ), and A, B, C be partitions of Y . Suppose G is a coordinate and G = {A, B,C} and A 6= B and B 6= C and C 6= A. Then ¬∀∀a,AG,BG ⋐ ∃∃¬a,BG,AG.
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