Groupwise density and the cofinality of the infinite symmetric group |
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Authors: | Simon Thomas |
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Institution: | (1) Mathematics Department, Rutgers University, New Brunswick, NJ 08903, USA , US |
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Abstract: | We study the relationship between the cofinality of the infinite symmetric group and the cardinal invariants and . 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
$c(Sym(\omega)) = \omega_{1}$
.
Received: 7 March 1996 |
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Keywords: | |
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