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arXiv · 1404.0080

Algorithm and proof as Ω-invariance and transfer: A new model of computation in nonstandard analysis

Sam Sanders
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Abstract

We propose a new model of computation based on nonstandard analysis. Intuitively, the role of "algorithm" is played by a new notion of finite procedure, called Omega-invariance and inspired by physics, from nonstandard analysis. Moreover, the role of 'proof' is taken up by the Transfer Principle from nonstandard analysis. We obtain a number of results in Constructive Reverse Mathematics to illustrate the tight correspondence to Errett Bishop's Constructive Analysis and the associated Constructive Reverse Mathematics.

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Sam Sanders. 2014-04-01. Algorithm and proof as Ω-invariance and transfer: A new model of computation in nonstandard analysis. https://doi.org/10.4204/eptcs.143.9

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