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The Problem of Determinacy of Infinite Games from an Intuitionistic Point of View

  • Wim Veldman
Part of the Logic, Epistemology, and the Unity of Science book series (LEUS, volume 15)

Abstract

Taking Brouwer's intuitionistic standpoint, we examine finite and infinite games of perfect information for players I and II. If one understands the disjunction occurring in the classical notion of determinacy constructively, even finite games are not always determinate. We therefore suggest an intuitionistically different notion of determinacy and prove that every subset of Cantor space is determinate in the proposed sense. Our notion is biased and considers games from the viewpoint of player I. In Cantor space, both player I and player II have two alternative possibilities for each move. It turns out that every subset of a space, where player II has, for each one of his moves, no more than a finite number of alternative possibilities while player I perhaps has infinitely many choices, is determinate in the proposed sense from the viewpoint of player I.

Keywords

Natural Number Winning Strategy Classical Point Baire Space Cantor Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science + Business Media B.V. 2009

Authors and Affiliations

  • Wim Veldman
    • 1
  1. 1.Institute for Mathematics, Astrophysics and Particle Physics Radboud University NijmegenNijmegenThe Netherlands

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