Wszystkie pola: Daniels, Peg - Katalog OPAC zbiorów

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Tytuł:: On the open-open game
Autorzy:: Daniels, Peg
Kunen, Kenneth
Zhou, Haoxuan
Powiązania:: https://bibliotekanauki.pl/articles/1208447.pdf
Data publikacji:: 1994
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Opis:: 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.
Źródło:: Fundamenta Mathematicae; 1994, 145, 3; 205-220
0016-2736
Pojawia się w:: Fundamenta Mathematicae
Dostawca treści:: Biblioteka Nauki

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