Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 46, Number 4 (2005), 407-417.
Polynomially Bounded Recursive Realizability
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.
Notre Dame J. Formal Logic, Volume 46, Number 4 (2005), 407-417.
First available in Project Euclid: 12 December 2005
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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