2014/04/01 by Sam Sanders
Computer Science · Mathematics · #cs.LO #math.LO
paper · pdf · doi:10.4204/eptcs.143.9
published as EPTCS 143, 2014, pp. 97-109 · In Proceedings DCM 2012, arXiv:1403.7579
arxiv created 2014/04/01 · arxiv updated 2014/04/02
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.