Algorithm and proof as \Omega-invariance and transfer: A new model of computation in nonstandard analysis
Logic in Computer Science
2014-04-02 v1 Logic
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.
Keywords
Cite
@article{arxiv.1404.0080,
title = {Algorithm and proof as \Omega-invariance and transfer: A new model of computation in nonstandard analysis},
author = {Sam Sanders},
journal= {arXiv preprint arXiv:1404.0080},
year = {2014}
}
Comments
In Proceedings DCM 2012, arXiv:1403.7579