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Some remarks on category of the real line

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Abstract.

We find a characterization of the covering number \(cov({\mathbb R})\), of the real line in terms of trees. We also show that the cofinality of \(cov({\mathbb R})\) is greater than or equal to \({\mathfrak n}_\lambda\) for every \(\lambda \in cov({\mathbb R}),\) where \(\mathfrak n_\lambda \geq add({\mathcal L})\) (\(add( {\mathcal L})\) is the additivity number of the ideal of all Lebesgue measure zero sets) is the least cardinal number k for which the statement: \((\exists{\mathcal G}\in [^\omega \omega ]^{\leq \lambda })(\forall{\mathcal F}\in [^\omega \omega ]^{\leq k})(\exists g\in{\mathcal G})(\exists h\in ^\omega \omega )(\forall f\in{\mathcal F})(\forall ^\infty n)(\exists u\in [g(n),g(n+1))(f(u)=h(u))\) fails.

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Received: 19 October 1994 / Revised version: 12 December 1996

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Keremedis, K. Some remarks on category of the real line. Arch Math Logic 38, 153–162 (1999). https://doi.org/10.1007/s001530050121

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  • DOI: https://doi.org/10.1007/s001530050121

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