Every countably presented formal topology is spatial, classically

Journal of Symbolic Logic 71 (2):491-500 (2006)
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Abstract

By using some classical reasoning we show that any countably presented formal topology, namely, a formal topology with a countable axiom set, is spatial

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original Valentini, S. (2006) "Every inductively generated formal cover is spatial, classically". Journal of Symbolic Logic 71(2):491-500

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Citations of this work

Cantor theorem and friends, in logical form.Silvio Valentini - 2013 - Annals of Pure and Applied Logic 164 (4):502-508.
Constructive characterizations of bar subsets.Silvio Valentini - 2007 - Annals of Pure and Applied Logic 145 (3):368-378.
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Generalising the fan theorem.Silvio Valentini - 2017 - Mathematical Logic Quarterly 63 (1-2):85-93.
Spatiality and classical logic.Milena Stefanova & Silvio Valentini - 2011 - Mathematical Logic Quarterly 57 (4):432-440.

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References found in this work

Inductively generated formal topologies.Thierry Coquand, Giovanni Sambin, Jan Smith & Silvio Valentini - 2003 - Annals of Pure and Applied Logic 124 (1-3):71-106.
The problem of the formalization of constructive topology.Silvio Valentini - 2005 - Archive for Mathematical Logic 44 (1):115-129.
A Course in Mathematical Logic.Perry Smith - 1980 - Journal of Symbolic Logic 45 (2):378-379.
An Intuitionistic Version of Cantor's Theorem.Dario Maguolo & Silvio Valentini - 1996 - Mathematical Logic Quarterly 42 (1):446-448.

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