The stationary set splitting game

The stationary set splitting game is a game of perfect information of length 1 between two players, unsplit and split, in which unsplit chooses stationarily many countable ordinals and split tries to continuously divide them into two stationary pieces. We show that it is possible in ZFC to force a winning strategy for either player, or for neither. This gives a new counterexample to 2 2 maximality with a predicate for the nonstationary ideal on 1, and an example of a consistently undetermined game of length 1 with payoff definable in the second-order monadic logic of order. We also show that the determinacy of the game is consistent with Martin's Axiom but not Martin's Maximum. MSC2000: 03E35; 03E60 The stationary set splitting game (SG) is a game of perfect information of length 1 between two players, unsplit and split. In each round , unsplit either accepts or rejects . If unsplit accepts , then split puts into one of two sets A and B. If unsplit rejects then split does ...

• Type: Journal
• Year: 2008
• Where: MLQ
• Authors: Paul B. Larson, Saharon Shelah
• Keywords: Game, MLQ 2008, Perfect Information, Splitting Game