## Journal of Symbolic Logic

- J. Symbolic Logic
- Volume 49, Issue 2 (1984), 343-375.

### Banach Games

#### Abstract

Banach introduced the following two-person, perfect information, infinite game on the real numbers and asked the question: For which sets $A \subseteq \mathbf{R}$ is the game determined? ???? Rules: The two players alternate moves starting with player I. Each move $a_n$ is legal iff it is a real number and $0 < a_n$, and for $n > 1, a_n < a_{n - 1}$. The first player to make an illegal move loses. Otherwise all moves are legal and I wins iff $\sum a_n$ exists and $\sum a_n \in A$. 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 determinancy and the determinancy of other well-known and much-studied games.

#### Article information

**Source**

J. Symbolic Logic, Volume 49, Issue 2 (1984), 343-375.

**Dates**

First available in Project Euclid: 6 July 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.jsl/1183741538

**Mathematical Reviews number (MathSciNet)**

MR745366

**Zentralblatt MATH identifier**

0616.03028

**JSTOR**

links.jstor.org

#### Citation

Freiling, Chris. Banach Games. J. Symbolic Logic 49 (1984), no. 2, 343--375. https://projecteuclid.org/euclid.jsl/1183741538