Recursion and Complexity

1 and 2, and in the last Section 4 of this abstract I will outline very briefly some conclusions about recursion and complexity which I believe that they support. 1 Partial Algebras A (pointed) partial algebra is a structure of the form A = (A, 0, 1, Φ) = (A, 0, 1, {φA }φ∈Φ), (1) where 0, 1 are distinct points in the universe A, and for every φ ∈ Φ, φA : An A is a partial function of some arity n associated by the signature Φ with the symbol φ. Typical example is the structure of arithmetic N = (N, 0, 1, =, +, ·), which happens to be total, i.e., the symbols ‘=’, ‘+’ and ‘·’ are interpreted by total functions, the characteristic function of the identity in the first case, and addition This is an outline of a projected lecture, in which I will refer extensively to and draw conclusions from results already published in [2]; and to make it as self-contained as possible, it has been necessary to quote extensively from [2], including the verbatim repetition of s...

• Type: Conference
• Year: 2005
• Where: CIE
• Authors: Yiannis N. Moschovakis
• Keywords: CIE 2005, Distinct Points, Partial Algebra, {φA }φ∈Φ