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Banach games

Published online by Cambridge University Press:  12 March 2014

Chris Freiling
Chris Freiling*
Affiliation:
University of California, Santa Barbara, California 93106
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Abstract

Abstract.

Banach introduced the following two-person, perfect information, infinite game on the real numbers and asked the question: For which sets A ⊆ R is the game determined?

Rules: The two players alternate moves starting with player I. Each move an is legal iff it is a real number and 0 < an, and for n > 1, an < an−1. The first player to make an illegal move loses. Otherwise all moves are legal and I wins iff exists and .

We will look at this game and some variations of it, called Banach games. In each case we attempt to find the relationship between Banach determinacy and the determinacy of other well-known and much-studied games.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 49 , Issue 2 , June 1984 , pp. 343 - 375
Copyright
Copyright © Association for Symbolic Logic 1984

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References

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