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A note on Brouwer's weak continuity principle and the transfer principle in nonstandard analysis
Stockholm University, Faculty of Science, Department of Mathematics.
2012 (English)In: Journal of Logic and Analysis, ISSN 1759-9008, E-ISSN 1759-9008, Vol. 4, no 2, 1-7 p.Article in journal (Refereed) Published
Abstract [en]

A wellknown model of nonstandard analysis is obtained by extending the structure of real numbers using an ultrapower construction. A constructive approach due to Schmieden and Laugwitz uses instead a reduced power construction modulo a cofinite filter, but has the drawback that the transfer principle is weak. In this paper it is shown that this principle can be strengthened by employing Brouwerian continuity axioms familiar from intuitionistic systems. We end by commenting on the relation between the transfer principle and Ishihara’s boundedness principle.

Place, publisher, year, edition, pages
2012. Vol. 4, no 2, 1-7 p.
Keyword [en]
intuitionistic mathematics, nonstandard analysis, transfer principle
National Category
Natural Sciences Algebra and Logic
Research subject
Mathematical Logic
Identifiers
URN: urn:nbn:se:su:diva-85901DOI: 10.4115/jla.2012.4.2OAI: oai:DiVA.org:su-85901DiVA: diva2:585337
Funder
Swedish Research Council
Available from: 2013-01-09 Created: 2013-01-09 Last updated: 2017-12-06Bibliographically approved

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