Abstract
We consider a question of T. Jech and K. Prikry that asks if the existence of a precipitous filter implies the existence of a normal precipitous filter. The aim of this paper is to improve a result of Gitik (Israel J Math, 175:191–219, 2010) and to show that measurable cardinals of a higher order rather than just measurable cardinals are necessary in order to have a model with a precipitous filter but without a normal one.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Donder H.-D., Levinski J.-P.: Weakly precipitous filters. Israel J. Math. 67(2), 225–242 (1989)
Ferber A., Gitik M.: On almost precipitous ideals. Arch. Math. Logic 49, 301–328 (2010)
Gitik M.: On normal precipitous ideals. Israel J. Math 175, 191–219 (2010)
Jech T., Prikry K.: On ideals of sets and the power set operation. Bull. Am. Math. Soc. 82(4), 593–595 (1976)
Mitchell W.: Applications of the covering lemma for sequences of measures. Trans. Am. Math. Soc. 299(1), 41–58 (1987)
Mitchell, W.: Beginning inner model theory. Handb. Set Theory 3(17), 1449–1496 (Springer, 2009)
Mitchell, W.: The covering lemma. Handb. Set Theory 3(18), 1497–1594, (Springer, 2009)
Schimmerling E., Velickovic B.: Collapsing functions. Math. Logic Quart. 50, 3–8 (2004)
Zeman M.: Inner models and large cardinals, de Gruyter series in logic and its applications. Vol. 5, Walter de Gruyter & Co, Berlin (2002)
Author information
Authors and Affiliations
Corresponding author
Additional information
Moti Gitik—partly by ISF Grant 234/08.
Rights and permissions
About this article
Cite this article
Gitik, M., Tal, L. On the strength of no normal precipitous filter. Arch. Math. Logic 50, 223–243 (2011). https://doi.org/10.1007/s00153-010-0211-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00153-010-0211-x