{"title":"算法与证明Ω-invariance与传递:一种新的非标准分析计算模型","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":"{\"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}","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}
Algorithm and proof as Ω-invariance and transfer: A new model of computation in nonstandard analysis
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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