A very weak distributive law and a related game in Boolean algebras.
by
Natasha Dobrinen
Penn State University

We will present a generalized notion of weak distributivity due to Prikry, namely the hyper-weak(\kappa, \lambda)-distributive law, give a forcing equivalence, define a related game, and show that for certain pairs of cardinal numbers, the hyper-weak (\kappa, \lambda)-distributive law is equivalent to the non-existence of a winning strategy for the first player in the game. It is consistent with ZFC that, for all \kappa >= \lambda, this game is undetermined, via \kappa⁺-Suslin trees.

Date received: March 9, 2003