团队游戏、超图空间和投影布尔代数
Team games, hypergraph spaces, and projective Boolean algebras
摘要：
我们修改的游戏Fuchino，Koppelberg，和Shelah用于表征的$κ$ -自由民族属性为一个给定的布尔代数$A$，更换球员I和II每个与一个团队的$n$球员有限的信息。我们表明，$A$是紧密的$κ$过滤时，团队II有一个获胜的策略，每一个有限的团队规模。$κ=\aleph_0$情形刻画了投射布尔代数和Dugundji空间。就丹尼尔斯、库宁和周小川的开放式比赛而言，这种定性是一个非常有利于我的团队版本。我们同样的特点科恩代数的一个团队版本的I-可扩展性。如果$A$是$κ^{+n}$上的$n$ -一致超图空间的闭根代数，避免了$[n+1]^n$的副本，那么团队II对于团队规模为$n-1$但不是$n$的修改后的FKS游戏有获胜策略。对于$n\geq 3$，这个代数也回答了一个问题Geschke结合时，一个本地${<}κ$大小的表征紧密$κ$过滤布尔代数，我们证明。案例$κ=\aleph_0$包含了投射布尔代数的局部有限刻画。
英文摘要：
We modify the game Fuchino, Koppelberg, and Shelah used to characterize the $κ$-Freese-Nation property for a given Boolean algebra $A$, replacing players I and II each with a team of $n$ players with limited information. We show that $A$ is tightly $κ$-filtered exactly when team II has a winning strategy for every finite team size. Case $κ=\aleph_0$ characterizes projective Boolean algebras and, hence, Dugundji spaces. In terms of the open-open game of Daniels, Kunen, and Zhou, this characterization is a team version of very I-favorable. We similarly characterize Cohen algebras in terms of a team version of I-favorability. If $A$ is the clopen algebra of the space of $n$-uniform hypergraphs on $κ^{+n}$ that avoid copies of $[n+1]^n$, then team II has a winning strategy for our modified FKS game for team size $n-1$ but not $n$. For $n\geq 3$, this algebra also answers a question of Geschke when combined with a locally ${<}κ$-sized characterization of tightly $κ$-filtered Boolean algebras that we prove. Case $κ=\aleph_0$ includes a locally finite characterization of projective Boolean algebras.
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。
