The canonical function game

Archive for Mathematical Logic 44 (7):817-827 (2005)

Abstract

The canonical function game is a game of length ω1 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 Σ22 absoluteness, cardinality spectra and Π2 maximality for H relative to the Continuum Hypothesis.

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References found in this work

Games of Length Ω1.Itay Neeman - 2007 - Journal of Mathematical Logic 7 (1):83-124.
Bounding by Canonical Functions, with Ch.Paul Larson & Saharon Shelah - 2003 - Journal of Mathematical Logic 3 (02):193-215.

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Citations of this work

Some Results About (+) Proved by Iterated Forcing.Tetsuya Ishiu & Paul B. Larson - 2012 - Journal of Symbolic Logic 77 (2):515-531.
Games of Length Ω1.Itay Neeman - 2007 - Journal of Mathematical Logic 7 (1):83-124.
The Stationary Set Splitting Game.Paul B. Larson & Saharon Shelah - 2008 - Mathematical Logic Quarterly 54 (2):187-193.
Provably Games.J. P. Aguilera & D. W. Blue - forthcoming - Journal of Symbolic Logic:1-22.
The Nonstationary Ideal in the Pmax Extension.Paul B. Larson - 2007 - Journal of Symbolic Logic 72 (1):138 - 158.

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