Real Analysis Exchange

An infinite game on groups.

Liljana Babinkostova and Marion Scheepers

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We consider an infinite game on a group $G$, defined relative to a subset $A$ of $G$. The game is denoted $\mathsf{G}(G,A)$. The finite version of the game, introduced in [1], was inspired by an attack on the RSA crypto-system as used in an implementation of SSL. Besides identifying circumstances under which player TWO does not have a winning strategy, we show for the topological group of real numbers that if $C$ is a set of real numbers having a selection property (*) introduced by Gerlits and Nagy, then for any interval $J$ of positive length, TWO has a winning strategy in the game $\mathsf{G}(\mathbb{R},J \cup C)$

Article information

Real Anal. Exchange, Volume 29, Number 2 (2003), 739-754.

First available in Project Euclid: 7 June 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03E17: Cardinal characteristics of the continuum 20F99: None of the above, but in this section 91A05: 2-person games

Game group winning strategy selection principle


Babinkostova , Liljana; Scheepers , Marion. An infinite game on groups. Real Anal. Exchange 29 (2003), no. 2, 739--754.

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