The Principle of Open Induction on Cantor space and the Approximate-Fan Theorem

Autor:	Veldman, Wim
Rok vydání:	2014
Předmět:	Mathematics - Logic 03F55 03F35
Druh dokumentu:	Working Paper
Popis:	The paper is a contribution to intuitionistic reverse mathematics. We work in a weak formal system for intuitionistic analysis. 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. The Approximate-Fan Theorem is an extension of the Fan Theorem that follows from Brouwer's principle of induction on bars in Baire space and implies the Principle of Open Induction on Cantor space. The Principle of Open Induction in Cantor space implies the Fan Theorem, but, conversely the Fan Theorem does not prove the Principle of Open Induction on Cantor space. We list a number of equivalents of the Principle of Open Induction on Cantor space and also a number of equivalents of the Approximate-Fan Theorem. Comment: 45 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1408.2493 Zobrazit plný text záznamu View this record from Arxiv