{"title":"On the connection between Nonstandard Analysis and Constructive Analysis","authors":"Sam Sanders","doi":"10.14288/1.0348311","DOIUrl":null,"url":null,"abstract":"Constructive Analysis and Nonstandard Analysis are often characterized as completely antipodal approaches to analysis. We discuss the possibility of capturing the central notion of Constructive Analysis (i.e. algorithm, finite procedure or explicit construction) by a simple concept inside Nonstandard Analysis. To this end, we introduce Omega-invariance and argue that it partially satisfies our goal. Our results provide a dual approach to Erik Palmgren's development of Nonstandard Analysis inside constructive mathematics.","PeriodicalId":46471,"journal":{"name":"Logique et Analyse","volume":"86 6 1","pages":"183-210"},"PeriodicalIF":0.3000,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Logique et Analyse","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.14288/1.0348311","RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Arts and Humanities","Score":null,"Total":0}
引用次数: 2
Abstract
Constructive Analysis and Nonstandard Analysis are often characterized as completely antipodal approaches to analysis. We discuss the possibility of capturing the central notion of Constructive Analysis (i.e. algorithm, finite procedure or explicit construction) by a simple concept inside Nonstandard Analysis. To this end, we introduce Omega-invariance and argue that it partially satisfies our goal. Our results provide a dual approach to Erik Palmgren's development of Nonstandard Analysis inside constructive mathematics.
期刊介绍:
Logique et Analyse is the continuation of Bulletin Intérieur, which was published from 1954 on by the Belgian National Centre for Logical Investigation, and intended originally only as an internal publication of results for its members and collaborators. Since the start of the new series, in 1958, however, the journal has been open to external submissions (and subscriptions). Logique et Analyse itself subscribes to no particular logical or philosophical doctrine, and so is open to articles from all points of view, provided only that they concern the designated subject matter of the journal.