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• W2952619047 abstract "We introduce constructive and classical systems for nonstandard arithmetic and show how variants of the functional interpretations due to Goedel and Shoenfield can be used to rewrite proofs performed in these systems into standard ones. These functional interpretations show in particular that our nonstandard systems are conservative extensions of extensional Heyting and Peano arithmetic in all finite types, strengthening earlier results by Moerdijk, Palmgren, Avigad and Helzner. We will also indicate how our rewriting algorithm can be used for term extraction purposes. To conclude the paper, we will point out some open problems and directions for future research and mention some initial results on saturation principles." @default.
• W2952619047 created "2019-06-27" @default.
• W2952619047 creator A5040167167 @default.
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• W2952619047 date "2011-09-14" @default.
• W2952619047 modified "2023-10-01" @default.
• W2952619047 title "A functional interpretation for nonstandard arithmetic" @default.
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• W2952619047 hasPublicationYear "2011" @default.
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