Algorithm and proof as Ω-invariance and transfer: A new model of computation in nonstandard analysis
arXiv:1404.0080 · doi:10.4204/EPTCS.143.9
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.
In Proceedings DCM 2012, arXiv:1403.7579