Brouwer's fan theorem as an axiom and as a contrast to Kleene's alternative

DOI10.1007/s00153-014-0384-9zbMath1327.03046arXiv1106.2738OpenAlexW1979862983WikidataQ114018316 ScholiaQ114018316MaRDI QIDQ403410

Wim Veldman

Publication date: 29 August 2014

Published in: Archive for Mathematical Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.2738

zbMATH Keywords

Baire spacecompactreal numbersBrouwer's fan theoremclosed-and-separableintuitionistic reverse mathematicsKleene's alternativepositively non-compact

Mathematics Subject Classification ID

Constructive and recursive analysis (03F60) Convergence and divergence of series and sequences (40A05) Foundations of classical theories (including reverse mathematics) (03B30) Second- and higher-order arithmetic and fragments (03F35) Intuitionistic mathematics (03F55)

Related Items (20)

Bounded inductive dichotomy: separation of open and clopen determinacies with finite alternatives in constructive contexts ⋮ A MARRIAGE OF BROUWER’S INTUITIONISM AND HILBERT’S FINITISM I: ARITHMETIC ⋮ Brouwer's fan theorem as an axiom and as a contrast to Kleene's alternative ⋮ EXTENDED FRAMES AND SEPARATIONS OF LOGICAL PRINCIPLES ⋮ Retracing Cantor's first steps in Brouwer's company ⋮ A constructive picture of Noetherian conditions and well quasi-orders ⋮ The uniform boundedness theorem and a boundedness principle ⋮ The binary expansion and the intermediate value theorem in constructive reverse mathematics ⋮ The anti-Specker property, a Heine-Borel property, and uniform continuity ⋮ The Monotone Completeness Theorem in Constructive Reverse Mathematics ⋮ Validating Brouwer's continuity principle for numbers using named exceptions ⋮ Kronecker's density theorem and irrational numbers in constructive reverse mathematics ⋮ Intuitionistic sequential compactness? ⋮ The creating subject, the Brouwer-Kripke schema, and infinite proofs ⋮ Equivalents of the finitary non-deterministic inductive definitions ⋮ Intuitionism: an inspiration? ⋮ Problems, solutions, and completions ⋮ Semantical completeness of first-order predicate logic and the weak fan theorem ⋮ Bishop-Style Constructive Reverse Mathematics ⋮ THE PREHISTORY OF THE SUBSYSTEMS OF SECOND-ORDER ARITHMETIC

Cites Work

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