Annals of Pure and Applied Logic 54 (3):195-227 (1991)

Abstract
We study various aspects of the size, including the cardinality, of closed unbounded subsets of [λ]<κ, especially when λ = κ+n for n ε ω. The problem is resolved into the study of the size of certain stationary sets. Relative to the existence of an ω1-Erdös cardinal it is shown consistent that ωω3 < ωω13 and every closed unbounded subsetof [ω3]<ω2 has cardinality ωω13. A weakening of the ω1-Erdös property, ω1-remarkability, is defined and shown to be retained under a large class of Easton-like forcings applied to ω1-Erdös cardinals. A class of reverse-Easton forcings preserving α-Erdösness is also described, with special attention to the establishment of □-principles. Article Outline
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DOI 10.1016/0168-0072(91)90047-p
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References found in this work BETA

The Core Model.A. Dodd & R. Jensen - 1981 - Annals of Mathematical Logic 20 (1):43-75.
Saturated Ideals.Kenneth Kunen - 1978 - Journal of Symbolic Logic 43 (1):65-76.
Forcing Closed Unbounded Sets.Uri Abraham & Saharon Shelah - 1983 - Journal of Symbolic Logic 48 (3):643-657.
Adding a Closed Unbounded Set.J. E. Baumgartner, L. A. Harrington & E. M. Kleinberg - 1976 - Journal of Symbolic Logic 41 (2):481-482.
A Strengthening of Jensen's □ Principles.Aaron Beller & Ami Litman - 1980 - Journal of Symbolic Logic 45 (2):251-264.

View all 7 references / Add more references

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On the Existence of Skinny Stationary Subsets.Yo Matsubara, Hiroshi Sakai & Toshimichi Usuba - 2019 - Annals of Pure and Applied Logic 170 (5):539-557.

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