A Completeness Theorem for “ Total Boolean Functions ” July 2008
نویسندگان
چکیده
0. Introduction. Even though the question answered in this note has its roots in denotational semantics for the differential λ-calculus ([2] and [1], see also [4]), no background in proof-theory is necessary to understand the problem. In the end, it boils down to a question about a special kind of polynomials in 2n variables over an arbitrary field k. This note is almost “self-contained”, assuming only mild knowledge about polynomials and vector spaces (and a modicum about affine spaces). The only exotic (??) technology is the following formula for counting monomials or multisets. The number of different monomials of degree d over n variables is usually denoted ( n d )
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