Real Analysis Exchange

An infinite game on groups.

Liljana Babinkostova and Marion Scheepers

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 7 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.rae/1149698536

Mathematical Reviews number (MathSciNet)
MR2083809

Zentralblatt MATH identifier
1065.03026

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

Keywords
Game group winning strategy selection principle

Citation

Babinkostova , Liljana; Scheepers , Marion. An infinite game on groups. Real Anal. Exchange 29 (2003), no. 2, 739--754. https://projecteuclid.org/euclid.rae/1149698536


Export citation

References

  • L. Babinkostova and M. Scheepers, A game on groups and information security, Proceedings of the Third International Conference for Informatics and Information Technologies - 2002, to appear.
  • J. A. Gallian, Contemporary Abstract Algebra 4th edition, Houghton Mifflin Company, 1998.
  • F. Galvin and A. W. Miller, On $\gamma$-sets and other singular sets of real numbers, Topology and its Applications, 17 (1984), 145–155.
  • Gerlits and Nagy, Some properties of C(X), I, Topology and its Applications, 14 (1982), 151–161.
  • W. Just, A. W. Miller, M. Scheepers and P. J. Szeptycki, The Combinatorics of open covers (II), Topology and its Applications, 73 (1996), 241–266.
  • A. Nowik, M. Scheepers and T. Weiss, The algebraic sum of sets of real numbers with strong measure zero sets, The Journal of Symbolic Logic, 63 (1998), 301–324.
  • F. Rothberger, Eine Verschärfung der Eigenschaft \sf C, Fundamenta Mathematicae, 30 (1938), 50–55.
  • M. Scheepers, Combinatorics of open covers (I): Ramsey Theory, Topology and its Applications, 69 (1996), 31–62.
  • T. Weiss, On finite products of special sets of real numbers, preprint.