Groupwise density and the cofinality of the infinite symmetric group

Archive for Mathematical Logic 37 (7):483-493 (1998)
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We study the relationship between the cofinality $c(Sym(\omega))$ of the infinite symmetric group and the cardinal invariants $\frak{u}$ and $\frak{g}$ . In particular, we prove the following two results. Theorem 0.1 It is consistent with ZFC that there exists a simple $P_{\omega_{1}}$ -point and that $c(Sym(\omega)) = \omega_{2} = 2^{\omega}$ . Theorem 0.2 If there exist both a simple $P_{\omega_{1}}$ -point and a $P_{\omega_{2}}$ -point, then $c(Sym(\omega)) = \omega_{1}$



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[Omnibus Review].Kenneth Kunen - 1969 - Journal of Symbolic Logic 34 (3):515-516.

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