On the Persistent Difficulty of Disjunction
- 147 Downloads
We want to show, in this paper, that, in intuitionistic analysis, the union of two closed subsets of Baire space N is not always closed, and that, more generally, the union of a closed set and a II n 0 -set is not always II n+1 0 . In the proof of this fact we make use of the intuitionistic Borel Hierarchy Theorem, established in (Veldman, 1981) and (Veldman, 2001a).
KeywordsNatural Number Infinite Sequence Convergent Sequence Winning Strategy Baire Space
Unable to display preview. Download preview PDF.
- Kleene, S. C. and Vesley, R. E. (1965). The Foundations of Intuitionistic Mathematics, Especially in Relation to Recursive Functions. North-Holland, Amsterdam.Google Scholar
- Troelstra, A. S. and van Dalen, D. (1988). Constructivism in Mathematics, volume I. North-Holland, Amsterdam.Google Scholar
- Veldman, W. (1981). Investigations in Intuitionistic Hierarchy Theory, Ph.D. Thesis. Katholieke Universiteit Nijmegen, Nijmegen.Google Scholar
- Veldman, W. (2001a). The Borel hierarchy and the projective hierarchy in intuitionistic mathematics, Report No. 0103, Department of Mathematics, Katholieke Universiteit Nijmegen, Nijmegen.Google Scholar
- Veldman, W. (2001b). Understanding and using Brouwer’s continuity principle. In: Berger, U., Osswald, P. and Schuster, P., editors, Reuniting the Antipodes, Constructive and Nonstandard Views of the Continuum. Proceedings of a Conference held in San Servolo/Venice, 1999, pp. 285–302. Kluwer Academic Press, Dordrecht.Google Scholar