The canonical function game

The canonical function game is a game of length 1 introduced by W. Hugh Woodin which falls inside a class of games known as Neeman games. Using large cardinals, we show that it is possible to force that the game is not determined. We also discuss the relationship between this result and 2 2 absoluteness, cardinality spectra and 2 maximality for H(2) relative to the Continuum Hypothesis. MSC2000: 03E60; 03E50, 03D60 The canonical function game, introduced by W.H. Woodin, is a game of perfect information of length 1 between two players, whom we call Dominating and Undominated. In each round , Undominated plays a countable ordinal u(), and then Dominating plays , a wellordering of of ordertype greater than u() (if ; when is finite we require only that is a wellordering of ; the first moves are irrelevant to the outcome of the game). After all 1 rounds have been played, Dominating wins the run of the game if and only if there exists a club C 1 such that = (

• Type: Journal
• Year: 2005
• Where: AML
• Authors: Paul B. Larson
• Keywords: AML 2005, Canonical Function Game, Game, Hugh Woodin