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SEPARATING THE FAN THEOREM AND ITS WEAKENINGS

Published online by Cambridge University Press:  18 August 2014

ROBERT S. LUBARSKY  and
HANNES DIENER
ROBERT S. LUBARSKY
Affiliation:
DEPT. OF MATHEMATICAL SCIENCES FLORIDA ATLANTIC UNIVERSITY BOCA RATON, FL 33431, USAEmail: Robert.Lubarsky@alum.mit.edu
HANNES DIENER
Affiliation:
DEPARTMENT MATHEMATIK, FAK. IV EMMY-NOETHER-CAMPUS, WALTER-FLEX-STR. 3 UNIVERSITY OF SIEGEN 57068 SIEGEN, GERMANYEmail: diener@math.uni-siegen.de
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Abstract

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.

Keywords

fan theoremsKripke modelsforcingnon-standard modelsHeyting-valued models03C9003F5003F6003H05
Type
Articles
Information
The Journal of Symbolic Logic , Volume 79 , Issue 3 , September 2014 , pp. 792 - 813
Copyright
Copyright © The Association for Symbolic Logic 2014 

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