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Summer 1998 A Model of $\widehat{R}^2_3$ inside a Subexponential Time Resource
Eugenio Chinchilla
Notre Dame J. Formal Logic 39(3): 307-324 (Summer 1998). DOI: 10.1305/ndjfl/1039182248

Abstract

Using nonstandard methods we construct a model of an induction scheme called $\hat{R}^2_3$ inside a "resource" of the form $\{M(a) : M $ is a Turing machine of code $ \leq r , \mbox{ and } M(a)$ is calculated in less than $2^{\vert\vert a\vert\vert^r}\mbox{ steps}\}$, where $\vert x\vert$ means the length of the binary expansion of $x$ and $a,r$ are nonstandard parameters in a model of $S^1_3$. As a consequence we obtain a model theoretic proof of a witnessing theorem for this theory by functions computable in time $2^{\vert n\vert^{O(1)}}$, a result first obtained by Buss, Krajícek, and Takeuti using proof theory.

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Eugenio Chinchilla. "A Model of $\widehat{R}^2_3$ inside a Subexponential Time Resource." Notre Dame J. Formal Logic 39 (3) 307 - 324, Summer 1998. https://doi.org/10.1305/ndjfl/1039182248

Information

Published: Summer 1998
First available in Project Euclid: 6 December 2002

zbMATH: 0967.03049
MathSciNet: MR1741540
Digital Object Identifier: 10.1305/ndjfl/1039182248

Subjects:
Primary: 03F30
Secondary: 03C62 , 03D15 , 03H15 , 68Q15

Rights: Copyright © 1998 University of Notre Dame

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Vol.39 • No. 3 • Summer 1998
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