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- W1567191326 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 $2^{vertvert avertvert^r}mbox{ steps}}$, where $vert xvert$ 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 $2^{vert nvert^{O(1)}}$, a result first obtained by Buss, Krajícek, and Takeuti using proof theory." @default.
- W1567191326 created "2016-06-24" @default.
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- W1567191326 date "1998-07-01" @default.
- W1567191326 modified "2023-09-23" @default.
- W1567191326 title "A Model of $widehat{R}^2_3$ inside a Subexponential Time Resource" @default.
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- W1567191326 doi "https://doi.org/10.1305/ndjfl/1039182248" @default.
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