覆盖对策与Banach-Mazur对策：k-策略
Covering games and the Banach-Mazur game: k-tactics
摘要：
给定集合X的子集的自由理想J，我们考虑这样的游戏，其中玩家ONE扮演J的sigma完成的元素的递增序列，并且TWO试图通过每次从J扮演一个集合来覆盖该序列的并集。我们描述了玩家TWO具有获胜策略的各种条件，该策略仅使用关于ONE的最近k次移动的信息，并将其中的一些结果应用于Banach-Mazur博弈。
英文摘要：
Given a free ideal J of subsets of a set X, we consider games where player ONE plays an increasing sequence of elements of the sigma completion of J, and TWO tries to cover the union of this sequence by playing one set at a time from J. We describe various conditions under which player TWO has has a winning strategy that uses only information about the most recent k moves of ONE, and apply some of these results to the Banach-Mazur game.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
