Abstract.
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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Received: 7 March 1996
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Thomas, S. Groupwise density and the cofinality of the infinite symmetric group. Arch Math Logic 37, 483–493 (1998). https://doi.org/10.1007/s001530050109
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DOI: https://doi.org/10.1007/s001530050109