On the open-open game

• Autorzy: Peg Daniels , Kenneth Kunen , Haoxuan Zhou
• Języki publikacji: EN

Abstrakty

EN

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 I or II does or does not have a winning strategy. We investigate the games on trees and Boolean algebras in detail, completely characterizing the game for $ω_1$-trees. An undetermined game is also defined. (In contrast, it is still open whether there is an undetermined game using the definition due to Berner and Juhász.) Finally, we show that various variations on the game yield equivalent games.

Kategorie tematyczne

• 54D99: None of the above, but in this section
• 54A35: Consistency and independence results
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1994
• Tom: 145
• Numer: 3
• Strony: 205-220

Daty

wydano

1994

otrzymano

1991-06-28

poprawiono

1993-08-24

poprawiono

1994-01-31

Twórcy

autor

Peg Daniels

• Department of Mathematics, Auburn University, Auburn, Alabama 36849-5310, U.S.A.

autor

Kenneth Kunen

• Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53708-1313, U.S.A.

autor

Haoxuan Zhou

• Department of Mathematics, Incarnate Word College, 4301 Broadway, San Antonio, Texas 78209, U.S.A.

Bibliografia

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