English

More on the cut and choose game

Logic 2016-09-06 v1

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 BB then BB is semiproper. (2) If Nonempty has a winning strategy and BB has 202^{\aleph _0} -c.c. then Nonempty has a winning strategy in the descending chain game. (3) Cons (BB is 1\aleph _1-distributive implies Nonempty has a winning strategy in c&c on BB ) We also give some new examples of forcings where Nonempty has or does not have a winning strategy in c&c game.

Keywords

Cite

@article{arxiv.math/9403203,
  title  = {More on the cut and choose game},
  author = {Jindřich Zapletal},
  journal= {arXiv preprint arXiv:math/9403203},
  year   = {2016}
}
R2 v1 2026-07-22T17:54:42.701Z