Accession Number : AD0647899

Title :   NOTES TOWARDS AN AXIOMATIZATION OF INTUITIONISTIC ANALYSIS,

Corporate Author : HUGHES AIRCRAFT CO FULLERTON CALIF

Personal Author(s) : Myhill,John

Report Date : NOV 1966

Pagination or Media Count : 26

Abstract : Assuming the formalization of intuitionistic number theory to be completed and known (Kleene), this paper discusses the formalization of intuitionistic analysis (theory of free-choice sequences). Each of the two new central notions of intuitionistic analysis over and above those of intuitionistic number theory corresponds to the classical notion of number-theoretic function. Axioms to be postulated for these objects are considered. Attention is given to Kreisel's axiom system (Lectures in Modern Mathematics, 1964) which makes explicit the distinction between free-choice sequences and (computable) functions that Kleene's does not. It is shown that the argument leading to the 'purified' sequence is not valid because there is no such (Brouwer) free-choice sequence as alpha'. Kripke's scheme is shown to have as a consequence that the species of computable functions cannot be enumerated by a formula, i.e., for any formula A(n,x,y) with only three (numerical) free variables indicated.

Descriptors :   (*MATHEMATICAL LOGIC, *SEQUENCES(MATHEMATICS)), NUMBER THEORY, FUNCTIONAL ANALYSIS, IDENTITIES, METAMATHEMATICS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE