Brouwer's fan theorem as an axiom and as a contrast to Kleene's alternative
type: Item
instance of: scholarly article
title: Brouwer's fan theorem as an axiom and as a contrast to Kleene's alternative
zbMATH Open document ID: 1327.03046
author: Wim Veldman
published in: Archive for Mathematical Logic
publication date: 2014-08-29T00:00:00Z
full work available at URL: https://arxiv.org/abs/1106.2738
review text: The author has based his paper on a tailor-made formal system, called Basic Intuitionistic Mathematics (BIM), which resembles \textit{W. A. Howard} and \textit{G. Kreisel}'s system H [J. Symb. Log. 31, 325--358 (1966; Zbl 0156.00804)] and \textit{A. S. Troelstra} and \textit{D. van Dalen}'s system EL [Constructivism in mathematics. An introduction. Volume I. Amsterdam etc.: North-Holland (1988; Zbl 0653.03040); Constructivism in mathematics. An introduction. Volume II. Amsterdam etc.: North-Holland (1988; Zbl 0661.03047)]. On this basis, he gives numerous equivalents of Brouwer's fan theorem and of Kleene's alternative. Variants of Dini's theorem on the uniform convergence of sequences of continuous functions play a prominent role, as do adequate variations of `compact' and of its negation.
reviewed by: Peter Schuster
Mathematics Subject Classification ID: 03F60
Mathematics Subject Classification ID: 03F55
Mathematics Subject Classification ID: 03B30
Mathematics Subject Classification ID: 03F35
Mathematics Subject Classification ID: 40A05
zbMATH DE Number: 6335990
zbMATH Keywords: Brouwer's fan theorem
zbMATH Keywords: Kleene's alternative
zbMATH Keywords: intuitionistic reverse mathematics
zbMATH Keywords: compact
zbMATH Keywords: positively non-compact
zbMATH Keywords: closed-and-separable
zbMATH Keywords: Baire space
zbMATH Keywords: real numbers
MaRDI profile type: Publication
Wikidata QID: Q114018316
OpenAlex ID: W1979862983
arXiv ID: 1106.2738
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DOI: 10.1007/S00153-014-0384-9
description: scientific article; zbMATH DE number 6335990