
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 freechoice 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 numbertheoretic 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 freechoice 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) freechoice 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