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SEPARATING THE FAN THEOREM AND ITS WEAKENINGS II

Published online by Cambridge University Press:  25 July 2019

ROBERT S. LUBARSKY
Affiliation:
DEPARTMENT OF MATHEMATICAL SCIENCES FLORIDA ATLANTIC UNIVERSITY BOCA RATON, FL33431, USA E-mail:robert.lubarsky@alum.mit.edu
Corresponding

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. Earlier work showed all of these implications to be strict. Here we reprove one of the strictness results, using very different arguments. The technique used is a mixture of realizability, forcing in the guise of Heyting-valued models, and Kripke models.

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Copyright © The Association for Symbolic Logic 2019 

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