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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Bibliographic Details
Published in:The Journal of symbolic logic 2013-03, Vol.78 (1), p.39-56
Main Author: Lubarsky, Robert S.
Format: Article
Language:English
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
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Summary: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.
ISSN:0022-4812
1943-5886
DOI:10.2178/jsl.7801030