A coverage construction of the reals and the irrationals

Annals of Pure and Applied Logic 145 (2):176-203 (2007)
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Abstract

I modify the standard coverage construction of the reals to obtain the irrationals. However, this causes a jump in ordinal complexity from ω+1 to Ω

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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.

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