Abstract
AbstractWe 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.
Publisher
Cambridge University Press (CUP)
Reference31 articles.
1. Foundations of Constructive Mathematics
2. A note on non-extensional operations in connection with continuity and recursiveness
3. Lubarsky Robert and Diener Hannes , Principles weaker than BD-ℕ, submitted for publication.
4. Lietz Peter , From constructive mathematics to computable analysis via the realizability interpretation, Ph.D. thesis, Technische Universität Darmstadt, 2004, http://www.mathematik.tu-darmstadt.de/-streicher/THESES/lietz.pdf.gz.
Cited by
7 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Constructive aspects of Riemann’s permutation theorem for series;Logic Journal of the IGPL;2023-10-24
2. The Third Trick;Logical Methods in Computer Science;2022-08-09
3. On the Necessity of Some Topological Spaces;Revolutions and Revelations in Computability;2022
4. Notions of Cauchyness and metastability;Journal of Logic and Computation;2020-09-29
5. Intuitionistic sequential compactness?;Indagationes Mathematicae;2018-12