Publication date
November 1991
DOI Publisher
Published by Elsevier B.V. ISSN
0168-0072Abstract
AbstractWe 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
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