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2018 Almost compatible functions and infinite length games
Steven Clontz, Alan Dow
Rocky Mountain J. Math. 48(2): 463-483 (2018). DOI: 10.1216/RMJ-2018-48-2-463

Abstract

${\mathcal{A}}'(\kappa)$ asserts the existence of pairwise almost compatible finite-to-one functions $A\to \omega$ for each countable subset $A$ of $\kappa$. The existence of winning $2$-Markov strategies in several infinite-length games, including the Menger game on the one-point Lindelofication $\kappa^\dagger$ of $\kappa$, are guaranteed by ${\mathcal{A}}'(\kappa)$. ${\mathcal{A}}'(\kappa)$ is implied by the existence of cofinal Kurepa families of size $\kappa$, and thus, holds for all cardinals less than $\aleph _\omega$. It is consistent that ${\mathcal{A}}'({\aleph _\omega })$ fails; however, there must always be a winning $2$-Markov strategy for the second player in the Menger game on $\omega_\omega^\dagger$.

Citation

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Steven Clontz. Alan Dow. "Almost compatible functions and infinite length games." Rocky Mountain J. Math. 48 (2) 463 - 483, 2018. https://doi.org/10.1216/RMJ-2018-48-2-463

Information

Published: 2018
First available in Project Euclid: 4 June 2018

zbMATH: 06883476
MathSciNet: MR3809153
Digital Object Identifier: 10.1216/RMJ-2018-48-2-463

Subjects:
Primary: 91A44
Secondary: 03E35, 03E55

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 2 • 2018
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