MEAGER-NOWHERE DENSE GAMES (V): CODING STRATEGIES AGAIN
作者:
Marion Scheepers,
期刊:
Quaestiones Mathematicae
(Taylor Available online 1994)
卷期:
Volume 17,
issue 4
页码: 419-435
ISSN:1607-3606
年代: 1994
DOI:10.1080/16073606.1994.9631775
出版商: Taylor & Francis Group
关键词: 90D44
数据来源: Taylor
摘要:
Players ONE and TWO play the following game of length ω: In then-th inning ONE first chooses a meager subset of the real line; TWO responds with a nowhere dense set. TWO wins only if the union of TWO'S nowhere dense sets is exactly equal to the union of ONE'S first category sets. We prove that TWO has a winning strategy, even if TWO remembers only the most recent two moves each inning (Corollary 8). We show that in a closely related game, the assertion that TWO has a winning strategy depending on only the most recent two moves each inning is equivalent to a weak version of the Singular Cardinals Hypothesis (Theorem 1).
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