Galvin’s “Racing Pawns” Game, Internal Hyperarithmetic Comprehension, and the Law of Excluded Middle

Notre Dame Journal of Formal Logic 54 (2):233-252 (2013)
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We show that the fact that the first player wins every instance of Galvin’s “racing pawns” game 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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Subsystems of Second Order Arithmetic.Stephen G. Simpson - 1999 - Studia Logica 77 (1):129-129.
Indecomposable linear orderings and hyperarithmetic analysis.Antonio Montalbán - 2006 - Journal of Mathematical Logic 6 (1):89-120.

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