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A definitive improvement of a game-theoretic bound and the long tightness game

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The main goal of the paper is the full proof of a cardinal inequality for a space with points $${G_\delta }$$Gδ, obtained with the help of a long version of… Click to show full abstract

The main goal of the paper is the full proof of a cardinal inequality for a space with points $${G_\delta }$$Gδ, obtained with the help of a long version of the Menger game. This result, which improves a similar one of Scheepers and Tall, was already established by the authors under the Continuum Hypothesis. The paper is completed by few remarks on a long version of the tightness game.

Keywords: game; improvement game; definitive improvement; game theoretic; theoretic bound; tightness game

Journal Title: Acta Mathematica Hungarica
Year Published: 2017

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