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2013 Galvin’s “Racing Pawns” Game, Internal Hyperarithmetic Comprehension, and the Law of Excluded Middle
Chris Conidis, Noam Greenberg, Daniel Turetsky
Notre Dame J. Formal Logic 54(2): 233-252 (2013). DOI: 10.1215/00294527-1960488

Abstract

We show that the fact that the first player (“white”) wins every instance of Galvin’s “racing pawns” game (for countable trees) is equivalent to arithmetic transfinite recursion. Along the way we analyze the satisfaction relation for infinitary formulas, of “internal” hyperarithmetic comprehension, and of the law of excluded middle for such formulas.

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Chris Conidis. Noam Greenberg. Daniel Turetsky. "Galvin’s “Racing Pawns” Game, Internal Hyperarithmetic Comprehension, and the Law of Excluded Middle." Notre Dame J. Formal Logic 54 (2) 233 - 252, 2013. https://doi.org/10.1215/00294527-1960488

Information

Published: 2013
First available in Project Euclid: 21 February 2013

zbMATH: 1280.03015
MathSciNet: MR3028797
Digital Object Identifier: 10.1215/00294527-1960488

Subjects:
Primary: 03B30

Rights: Copyright © 2013 University of Notre Dame

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Vol.54 • No. 2 • 2013
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