{"title":"Algorithm and proof as Ω-invariance and transfer: A new model of computation in nonstandard analysis","authors":"Sam Sanders","doi":"10.4204/EPTCS.143.9","DOIUrl":null,"url":null,"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.","PeriodicalId":88470,"journal":{"name":"Dialogues in cardiovascular medicine : DCM","volume":"83 1","pages":"97-109"},"PeriodicalIF":0.0000,"publicationDate":"2014-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dialogues in cardiovascular medicine : DCM","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4204/EPTCS.143.9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
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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