On the cofinality of the splitting number. (English) Zbl 1436.03260
Summary: The splitting number \(\mathfrak{s}\) can be singular. The key method is to construct a forcing poset with finite support matrix iterations of ccc posets introduced by A. Blass and S. Shelah [Isr. J. Math. 65, No. 3, 259–271 (1989; Zbl 0681.03033)].
Citations:
Zbl 0681.03033References:
| [1] | Blass, Andreas; Shelah, Saharon, Ultrafilters with small generating sets, Israel J. Math., 65, 3, 259-271 (1989), MR1005010 (90e:03057) · Zbl 0681.03033 |
| [2] | Brendle, Jörg, The almost-disjointness number may have countable cofinality, Trans. Amer. Math. Soc., 355, 7, 2633-2649 (2003), (electronic), MR1975392 (2004c:03062) · Zbl 1061.03051 |
| [3] | Brendle, Jörg; Fischer, Vera, Mad families, splitting families and large continuum, J. Symbolic Logic, 76, 1, 198-208 (2011), MR2791343 (2012d:03113) · Zbl 1215.03061 |
| [4] | (Kunen, Kenneth; Vaughan, Jerry E., Handbook of Set-Theoretic Topology (1984), North-Holland Publishing Co.: North-Holland Publishing Co. Amsterdam), vii+1273, MR776619 (85k:54001) · Zbl 0674.54001 |
| [5] | Shelah, Saharon, The character spectrum of \(\beta(N)\), Topology Appl., 158, 18, 2535-2555 (2011), MR2847327 · Zbl 1312.03030 |
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