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Boise Extravaganza in Set Theory
March 27-29, 2009
Boise State University
Boise, Idaho, United States

Organizers
Liljana Babinkostova, Andrés E. Caicedo, Stefan Geschke, Richard Ketchersid and Marion Scheepers

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Scheepers's countable-finite game in models of determinacy
by
Andres Eduardo Caicedo
Boise State University
Coauthors: Richard Ketchersid

The countable-finite game is an infinite perfect information two-player game relative to a given set. Under choice, player II has an obvious winning strategy. In contrast, we show that in canonical models of AD+ any nontrivial instance of this game is undetermined.

This is obtained as a corollary of a general dichotomy theorem for sets X in canonical models of AD+, namely, either X is well-ordered or else the reals embed into X. The proof of the dichotomy result will be presented by Ketchersid.

Date received: March 21, 2009

Copyright © 2009 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 # cayb-10.