Determinateness in the low protective hierarchy
Harvey Friedman (1971)
Fundamenta Mathematicae
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Determinateness in the low protective hierarchy
On the open-open game
Peg Daniels, Kenneth Kunen, Haoxuan Zhou (1994)
Fundamenta Mathematicae
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We modify a game due to Berner and Juhász to get what we call “the open-open game (of length ω)”: a round consists of player I choosing a nonempty open subset of a space X and II choosing a nonempty open subset of I’s choice; I wins if the union of II’s open sets is dense in X, otherwise II wins. This game is of interest for ccc spaces. It can be translated into a game on partial orders (trees and Boolean algebras, for example). We present basic results and various conditions under which...
Measurable cardinals and analytic games
Donald Matrin (1970)
Fundamenta Mathematicae
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On the netweight of subspaces
Krzysztof Ciesielski (1983)
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Prioric games and minimal degrees below
C. Yates (1974)
Fundamenta Mathematicae
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On a game of Sierpiński
Grzegorz Kubicki (1987)
Colloquium Mathematicae
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G. Debs, J. Saint Raymond (1996)
Acta Universitatis Carolinae. Mathematica et Physica
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Galvin Tree-Games
E. C. Milner (1985)
Publications du Département de mathématiques (Lyon)
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Hercules versus Hidden Hydra Helper
Jiří Matoušek, Martin Loebl (1991)
Commentationes Mathematicae Universitatis Carolinae
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L. Kirby and J. Paris introduced the Hercules and Hydra game on rooted trees as a natural example of an undecidable statement in Peano Arithmetic. One can show that Hercules has a “short” strategy (he wins in a primitively recursive number of moves) and also a “long” strategy (the finiteness of the game cannot be proved in Peano Arithmetic). We investigate the conflict of the “short” and “long” intentions (a problem suggested by J. Nešetřil). After each move of Hercules (trying to kill...