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A CONSTRUCTIVE EXAMINATION OF A RUSSELL-STYLE RAMIFIED TYPE THEORY
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 12018 (English)In: Bulletin of Symbolic Logic, ISSN 1079-8986, E-ISSN 1943-5894, Vol. 24, no 1, p. 90-106Article in journal (Refereed) Published
Abstract [en]

In this article we examine the natural interpretation of a ramified type hierarchy into Martin-Lof type theory with an infinite sequence of universes. It is shown that under this predicative interpretation some useful special cases of Russell's reducibility axiom are valid, namely functional reducibility. This is sufficient to make the type hierarchy usable for development of constructive mathematical analysis in the style of Bishop. We present a ramified type theory suitable for this purpose. One may regard the results of this article as an alternative solution to the problem of the proliferation of levels of real numbers in Russell's theory, which avoids impredicativity, but instead imposes constructive logic. The intuitionistic ramified type theory introduced here also suggests that there is a natural associated notion of predicative elementary topos.

Place, publisher, year, edition, pages
2018. Vol. 24, no 1, p. 90-106
Keywords [en]
ramified type theory, intuitionistic logic, reducibility axiom
National Category
Mathematics Computer and Information Sciences
Identifiers
URN: urn:nbn:se:su:diva-156694DOI: 10.1017/bsl.2018.4ISI: 000431008000003OAI: oai:DiVA.org:su-156694DiVA, id: diva2:1211232
Available from: 2018-05-30 Created: 2018-05-30 Last updated: 2018-05-30Bibliographically approved

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