Original Publication Date
The Journal of Symbolic Logic
DOI of Original Publication
Date of Submission
It is well known that saturation of ideals is closely related to the “antichain-catching” phenomenon from Foreman-Magidor-Shelah . We consider several antichain-catching properties that are weaker than saturation, and prove: (1) If I is a normal ideal on ω2 which satisfies stationary antichain catching, then there is an inner model with a Woodin cardinal; (2) For any n ∈ ω, it is consistent relative to large cardinals that there is a normal ideal I on ωn which satisfies projective antichain catching, yet I is not saturated (or even strong). This provides a negative answer to Open Question number 13 from Foreman’s chapter in the Handbook of Set Theory ().
© 2013, Association for Symbolic Logic. This is the author’s version of a work that was accepted for publication in The Journal of Symbolic Logic, Volume 79, Issue 04, December 2014, pp 1247-1285. The final publication is available at http://dx.doi.org/10.1017/jsl.2013.24.
Is Part Of
VCU Mathematics and Applied Mathematics Publications