Abstract
For \({b \in {^{\omega}}{\omega}}\) , let \({\mathfrak{c}^{\exists}_{b, 1}}\) be the minimal number of functions (or slaloms with width 1) to catch every functions below b in infinitely many positions. In this paper, by using the technique of forcing, we construct a generic model in which there are many coefficients \({\mathfrak{c}^{\exists}_{{b_\alpha}, 1}}\) with pairwise different values. In particular, under the assumption that a weakly inaccessible cardinal exists, we can construct a generic model in which there are continuum many coefficients \({\mathfrak{c}^{\exists}_{{b_\alpha}, 1}}\) with pairwise different values. In conjunction with these results, we give a generic model in which there are many Yorioka’s ideals \({\mathcal{I}_{f_\alpha}}\) with pairwise different covering numbers.
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Osuga, N., Kamo, S. Many different covering numbers of Yorioka’s ideals. Arch. Math. Logic 53, 43–56 (2014). https://doi.org/10.1007/s00153-013-0354-7
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DOI: https://doi.org/10.1007/s00153-013-0354-7