2005 Polynomially Bounded Recursive Realizability
Saeed Salehi
Notre Dame J. Formal Logic 46(4): 407-417 (2005). DOI: 10.1305/ndjfl/1134397659
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.

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Copyright © 2005 University of Notre Dame
Saeed Salehi "Polynomially Bounded Recursive Realizability," Notre Dame Journal of Formal Logic 46(4), 407-417, (2005). https://doi.org/10.1305/ndjfl/1134397659
Published: 2005
JOURNAL ARTICLE
11 PAGES

Vol.46 • No. 4 • 2005