On the persistent difficulty of disjunction

Wim Veldman

pp. 77-90

in: Artur Rojszczak, Jacek Cachro, Gabriel Kurczewski (eds), Philosophical dimensions of logic and science, Berlin, Springer, 2003

Abstract

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+1⁰. In the proof of this fact we make use of the intuitionistic Borel Hierarchy Theorem, established in (Veldman, 1981) and (Veldman, 2001a).