Notre Dame Journal of Formal Logic

Polynomially Bounded Recursive Realizability

Saeed Salehi

Abstract

A polynomially bounded recursive realizability, in which the recursive functions used in Kleene's realizability are restricted to polynomially bounded functions, is introduced. It is used to show that provably total functions of Ruitenburg's Basic Arithmetic are polynomially bounded (primitive) recursive functions. This sharpens our earlier result where those functions were proved to be primitive recursive. Also a polynomially bounded schema of Church's Thesis is shown to be polynomially bounded realizable. So the schema is consistent with Basic Arithmetic, whereas it is inconsistent with Heyting Arithmetic.

Article information

Source
Notre Dame J. Formal Logic, Volume 46, Number 4 (2005), 407-417.

Dates
First available in Project Euclid: 12 December 2005

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1134397659

Digital Object Identifier
doi:10.1305/ndjfl/1134397659

Mathematical Reviews number (MathSciNet)
MR2183051

Zentralblatt MATH identifier
1097.03051

Subjects
Primary: 03F30: First-order arithmetic and fragments
Secondary: 03F50: Metamathematics of constructive systems

Keywords
provably total function Basic Arithmetic Basic Logic realizability

Citation

Salehi, Saeed. Polynomially Bounded Recursive Realizability. Notre Dame J. Formal Logic 46 (2005), no. 4, 407--417. doi:10.1305/ndjfl/1134397659. https://projecteuclid.org/euclid.ndjfl/1134397659


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