1994/03/10 by Jindřich Zapletal, Zapletal, Jindřich
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis #math.LO
paper · pdf · doi:10.48550/arxiv.math/9403203
arxiv created 1994/03/10 · openalex publication_date 1994/03/10 · arxiv updated 2016/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 2ℵ 0 -c.c. then Nonempty has a winning strategy in the descending chain game. (3) Cons (B is ℵ 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.