On the failure of BD-ℕ and BD, and an application to the anti-specker property

We give the natural topological model for ¬BD-ℕ, and use it to show that the closure of spaces with the anti-Specker property under product does not imply BD-ℕ. Also, the natural topological model for ¬BD is presented. Finally, for some of the realizability models known indirectly to falsify BD-ℕ, i...

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Veröffentlicht in:	The Journal of symbolic logic 2013-03, Vol.78 (1), p.39-56
1. Verfasser:	Lubarsky, Robert S.
Format:	Artikel
Sprache:	eng
Schlagworte:	Anti-Specker BD-ℕ Constructive mathematics Integers Logic Mathematical continuity Mathematical functions Mathematical logic Mathematical theorems Mathematics Natural numbers Philosophy Realizability topological models Topological spaces Topology
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container_title	The Journal of symbolic logic
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creator	Lubarsky, Robert S.
description	We give the natural topological model for ¬BD-ℕ, and use it to show that the closure of spaces with the anti-Specker property under product does not imply BD-ℕ. Also, the natural topological model for ¬BD is presented. Finally, for some of the realizability models known indirectly to falsify BD-ℕ, it is brought out in detail how BD-ℕ fails.
doi_str_mv	10.2178/jsl.7801030
format	Article
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subjects	Anti-Specker BD-ℕ Constructive mathematics Integers Logic Mathematical continuity Mathematical functions Mathematical logic Mathematical theorems Mathematics Natural numbers Philosophy Realizability topological models Topological spaces Topology
title	On the failure of BD-ℕ and BD, and an application to the anti-specker property
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