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

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 Ω-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.