论文标题
带有过滤器的游戏
Games with Filters
论文作者
论文摘要
本文有两个部分。第一个关注的是，我们称为\ emph {welch Games}的Holy and Schlicht引入的游戏系列。玩家II在$κ$上的长度$ω$的韦尔奇游戏中具有获胜策略相当于紧凑型。赢得$ 2^κ$的长度游戏相当于可衡量的$κ$。我们表明，对于中间长度$γ$的游戏，II获胜意味着存在$γ$ cluct的巨大理想，$γ$浓缩的树木。 第二部分显示第一个不是空置的。对于$ω$和$κ^+$之间的每条$γ$，它给出了II赢得长度$γ$的游戏，而不是$γ^+$。该技术还提供了模型，其中所有$ω_1<γ\leκ$都有$κ$ - complete，normal，$κ^+$ - 分布式理想，具有$γ$的密集套件，但没有$γ^+$ - 关闭。
This paper has two parts. The first is concerned with a variant of a family of games introduced by Holy and Schlicht, that we call \emph{Welch games}. Player II having a winning strategy in the Welch game of length $ω$ on $κ$ is equivalent to weak compactness. Winning the game of length $2^κ$ is equivalent to $κ$ being measurable. We show that for games of intermediate length $γ$, II winning implies the existence of precipitous ideals with $γ$-closed, $γ$-dense trees. The second part shows the first is not vacuous. For each $γ$ between $ω$ and $κ^+$, it gives a model where II wins the games of length $γ$, but not $γ^+$. The technique also gives models where for all $ω_1< γ\leκ$ there are $κ$-complete, normal, $κ^+$-distributive ideals having dense sets that are $γ$-closed, but not $γ^+$-closed.
