Wim Veldman
Published 2014-08-11, updated 2015-04-07Version 2
The paper is a contribution to intuitionistic reverse mathematics. The Principle of Open Induction on Cantor space is the statement that every open subset of Cantor space that is progressive with respect to the lexicographical ordering of Cantor space coincides with Cantor space. This principle follows from Brouwer's principle of induction on bars in Baire space and it implies the Fan Theorem. Working in a weak system for intuitionistic analysis we list a large number of equivalents of this principle, including an extension of the Fan Theorem called the Approximate-Fan Theorem. We prove that the Approximate-Fan Theorem is stronger than the Fan Theorem.
Comments: This paper has been withdrawn by the author. The proof of Theorem 6.2 is incorrect and the Theorem probably fails to be true
Projective sets, intuitionistically
Principles of bar induction and continuity on Baire space
Covering the Baire space by families which are not finitely dominating
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