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Constructivist and structuralist foundations: Bishop's and Lawvere's theories of sets
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry. Uppsala University, The Swedish Collegium for Advanced Study in the Social Sciences (SCASSS).
2012 (English)In: Annals of Pure and Applied Logic, ISSN 0168-0072, E-ISSN 1873-2461, Vol. 163, no 10, 1384-1399 p.Article in journal (Refereed) Published
Abstract [en]

Bishop's informal set theory is briefly discussed and compared to Lawvere's Elementary Theory of the Category of Sets (ETCS). We then present a constructive and predicative version of ETCS, whose standard model is based on the constructive type theory of Martin-Lof. The theory, CETCS, provides a structuralist foundation for constructive mathematics in the style of Bishop.

Place, publisher, year, edition, pages
2012. Vol. 163, no 10, 1384-1399 p.
Keyword [en]
Categories of sets, Categorical logic
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-181387DOI: 10.1016/j.apal.2012.01.011ISI: 000307415400004OAI: oai:DiVA.org:uu-181387DiVA: diva2:557704
Available from: 2012-09-28 Created: 2012-09-24 Last updated: 2017-12-07Bibliographically approved

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Algebra and GeometryThe Swedish Collegium for Advanced Study in the Social Sciences (SCASSS)
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Annals of Pure and Applied Logic
Mathematics

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