#
The ideal determined by the unsymmetric game

**Ludomir Newelski and Andrzej Roslanowski**
We study the -ideal
of subsets of the Baire space
for which the second player has a winning strategy in the unsymmetric game
(i.e. in the game in which Player I is allowed to play finite sequences
of integers while the second player answers by single integers). We prove
that the additivity number of this ideal is
and that the cofinality number (the minimal size of the basis of the ideal)
is .
Related ideals on compact spaces
(for )
are studied and some consistency results are obtained. Some new forcing
notions appear naturally here as well as new localization properties of
extensions of models of ZFC (like: ``each real
in the extension is an -branch
in a tree
from the ground model such that each node in the tree has at most *n*
successors'').

Andrzej Roslanowski
Back
to the list of my papers.