SEPARATING THE FAN THEOREM AND ITS WEAKENINGS

Varieties of the Fan Theorem have recently been developed in reverse constructive mathematics, corresponding to different continuity principles. They form a natural implicational hierarchy. Some of the implications have been shown to be strict, others strict in a weak context, and yet others not at...

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Bibliographic Details
Published in:The Journal of symbolic logic 2014-09, Vol.79 (3), p.792-813
Main Authors: LUBARSKY, ROBERT S., DIENER, HANNES
Format: Article
Language:English
Subjects:
Kripke, Saul
Logic
Mathematics
Philosophy
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Summary:Varieties of the Fan Theorem have recently been developed in reverse constructive mathematics, corresponding to different continuity principles. They form a natural implicational hierarchy. Some of the implications have been shown to be strict, others strict in a weak context, and yet others not at all, using disparate techniques. Here we present a family of related Kripke models which separates all of the as yet identified fan theorems.
ISSN:0022-4812
1943-5886
DOI:10.1017/jsl.2014.9