更多关于切割和选择游戏

摘要：

本文改进了Velickovic关于完备布尔代数上的cut and choose（c&c）博弈的一些结果. (1)如果Nonempty在$B$上的c&c博弈中有获胜策略，则$B$是半真的。(2)如果Nonempty有获胜策略，而$B$有$2^{\aleph _0}$ -c. c。那么Nonempty在下降链博弈中有获胜策略(3)缺点（$B$是$\aleph _1$ -分配的，意味着Nonempty在c&c中有一个获胜策略，关于$B$）我们还给出了Nonempty在c&c博弈中有或没有获胜策略的强迫的一些新例子。

英文摘要：

We improve some ancient results of Velickovic on the cut and choose (c&c) game on complete Boolean algebras. (1) If Nonempty has a winning strategy for c&c game on $B$ then $B$ is semiproper. (2) If Nonempty has a winning strategy and $B$ has $2^{\aleph _0}$ -c.c. then Nonempty has a winning strategy in the descending chain game. (3) Cons ($B$ is $\aleph _1$-distributive implies Nonempty has a winning strategy in c&c on $B$ ) We also give some new examples of forcings where Nonempty has or does not have a winning strategy in c&c 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。