Affiliation:
1. Department of Mathematics and Informatics, Novi Sad
Abstract
The games G2 and G3 are played on a complete Boolean algebra B in ?-many
moves. At the beginning White picks a non-zero element p of B and, in the
n-th move, White picks a positive pn < p and Black chooses an in ? {0,1}.
White wins G2 iff lim inf pin,n = 0 and wins G3 iff W A?[?]? ? n?A pin,n = 0.
It is shown that White has a winning strategy in the game G2 iff White has a
winning strategy in the cut-and-choose game Gc&c introduced by Jech. Also,
White has a winning strategy in the game G3 iff forcing by B produces a
subset R of the tree <?2 containing either ??0 or ??1, for each ? ? <?2, and
having unsupported intersection with each branch of the tree <?2 belonging
to V. On the other hand, if forcing by B produces independent (splitting)
reals then White has a winning strategy in the game G3 played on B. It is
shown that ? implies the existence of an algebra on which these games are
undetermined.
Publisher
National Library of Serbia