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Minimal readability of intuitionistic arithmetic and elementary analysis

Published online by Cambridge University Press:  12 March 2014

Zlatan Damnjanovic
Zlatan Damnjanovic*
Affiliation:
School of Philosophy, University of Southern California, Los Angeles, California 90089–0451
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Abstract

A new method of “minimal” readability is proposed and applied to show that the definable functions of Heyting arithmetic (HA)—functions f such that HA ⊢ ∀x∃!yA(x, y) ⇒ for all m, A(m, f(m)) is true, where A(x, y) may be an arbitrary formula of ℒ(HA) with only x,y free—are precisely the provably recursive functions of the classical Peano arithmetic (PA), i.e., the < ε0-recursive functions. It is proved that, for prenex sentences provable in HA, Skolem functions may always be chosen to be < ε0-recursive. The method is extended to intuitionistic finite-type arithmetic, , and elementary analysis. Generalized forms of Kreisel's characterization of the provably recursive functions of PA and of the no-counterexample-interpretation for PA are consequently derived.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 60 , Issue 4 , December 1995 , pp. 1208 - 1241
Copyright
Copyright © Association for Symbolic Logic 1995

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