Cantor theorem and friends, in logical form

Annals of Pure and Applied Logic 164 (4):502-508 (2013)

We prove a generalization of the hyper-game theorem by using an abstract version of inductively generated formal topology. As applications we show proofs for Cantor theorem, uncountability of the set of functions from N to N and Gödel theorem which use no diagonal argument
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DOI 10.1016/j.apal.2012.10.011
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Inductively Generated Formal Topologies.Thierry Coquand, Giovanni Sambin, Jan Smith & Silvio Valentini - 2003 - Annals of Pure and Applied Logic 124 (1-3):71-106.
Constructive Characterizations of Bar Subsets.Silvio Valentini - 2007 - Annals of Pure and Applied Logic 145 (3):368-378.

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