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Club guessing sequences and filters

Published online by Cambridge University Press:  12 March 2014

Tetsuya Ishiu
Tetsuya Ishiu*
Affiliation:
University of Kansas, Department of Mathematics, 405 SNOW Hall, 1460 Jayhawk Blvd, Lawrence, KS 66045, USA, E-mail: ishiu@math.ku.edu
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Abstract

We investigate club guessing sequences and filters. We prove that assuming V = L, there exists a strong club guessing sequence on μ if and only if μ is not ineffable for every uncountable regular cardinal μ. We also prove that for every uncountable regular cardinal μ, relative to the existence of a Woodin cardinal above μ, it is consistent that every tail club guessing ideal on μ is precipitous.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 70 , Issue 4 , December 2005 , pp. 1037 - 1071
Copyright
Copyright © Association for Symbolic Logic 2005

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