|
Abstract:
|
The method of forcing is widely used in set theory to obtain
various consistency proofs. Complete Boolean algebras play the main role
in applications of forcing. Therefore it is useful to define games on Boolean
algebras that characterize their properties important for the method. The
most investigated game is Jech’s distributivity game, such that the first
player has the winning strategy iff the algebra is not (!, 2)-distributive.
We define another game characterizing the collapsing of the continuum to
!, prove several sufficient conditions for the second player to have a winning
strategy, and obtain a Boolean algebra on which the game is undetermined. |