Adjoining dominating functions

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Journal of Symbolic Logic 50 (1):94-101 (1985)
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Abstract

If dominating functions in ω ω are adjoined repeatedly over a model of GCH via a finite-support c.c.c. iteration, then in the resulting generic extension there are no long towers, every well-ordered unbounded family of increasing functions is a scale, and the splitting number s (and hence the distributivity number h) remains at ω 1

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10.2307/2273792

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Citations of this work

Mathias–Prikry and Laver–Prikry type forcing.Michael Hrušák & Hiroaki Minami - 2014 - Annals of Pure and Applied Logic 165 (3):880-894.
Mad families, splitting families and large continuum.Jörg Brendle & Vera Fischer - 2011 - Journal of Symbolic Logic 76 (1):198 - 208.
Special ultrafilters and cofinal subsets of $$({}^omega omega, <^*)$$.Peter Nyikos - 2020 - Archive for Mathematical Logic 59 (7-8):1009-1026.
Forcing indestructibility of MAD families.Jörg Brendle & Shunsuke Yatabe - 2005 - Annals of Pure and Applied Logic 132 (2):271-312.
Splittings.A. Kamburelis & B. W’Glorz - 1996 - Archive for Mathematical Logic 35 (4):263-277.

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References found in this work

Set Theory.Keith J. Devlin - 1981 - Journal of Symbolic Logic 46 (4):876-877.

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