More on the cut and choose game

Jindřich Zapletal

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arXiv · math/9403203

More on the cut and choose game

Jindřich Zapletal

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Abstract

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.

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Jindřich Zapletal. 1994-03-10. More on the cut and choose game. https://arxiv.org/abs/math/9403203

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