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Multiple gaps and some finitizations of club and CH https://arxiv.org/abs/2504.15398 #mathLO #mathGN

Multiple gaps and some finitizations of club and CH

We continue the development of the theory of capturing schemes over $ω_1$ by analyzing the relation between the capturing construction schemes (whose existence is implied by Jensen's $\Diamond$-principle) and both the Continuum Hypothesis and Ostaszewski's $\clubsuit$-principle. Formally, we show that the property of being capturing can be viewed as the conjunction of two properties, one of which is implied by $\clubsuit$ and the other one by CH. We apply these principles to construct multiple gaps, entangled sets and metric spaces without uncountable monotone subspaces.

arXiv.org
April 24, 2025 at 3:10 AM · · feed2toot · 0 · 0 · 0
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