Predicting reals with trees
by
Masaru Kada
Kitami Institute of Technology

We say a forcing notion P has the k-ary Sacks property if, for every function f in \omega^\omega in the forcing model by P, there is a tree T subset or equal \omega ^{< \omega} in the ground model such that f is a branch through T and every node in T has up to k successors. It is easy to see that the k-ary Sacks property has distinct strength for each k < \omega and is strictly stronger than the original Sacks property. Using this notion, we investigate the relationship among various cardinal invariants associated with ``evasion and prediction'', which have been studied by Blass, Brendle, Shelah, Kamo and so on.

http://math.cs.kitami-it.ac.jp/~kada/

Date received: March 7, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagb-07.