Abstract
Given a regular cardinal κ > ω 1 and a cardinal λ with κ ≤ cf (λ) < λ, we show that NS κ,λ | T is not λ+-saturated, where T is the set of all \({a\in P_\kappa (\lambda)}\) such that \({| a | = | a \cap \kappa|}\) and \({{\rm cf} \big( {\rm sup} (a\cap\kappa)\big) = {\rm cf} \big({\rm sup} (a)\big) = \omega}\).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Burke D.R., Matsubara Y.: The extent of strength in the club filters. Israel J. Math. 114, 253–263 (1999)
Donder H.D., Matet P.: Two cardinal versions of diamond. Israel J. Math. 83, 1–43 (1993)
Foreman M., Magidor M.: Mutually stationary sequences of sets and the non-saturation of the non-stationnary ideal on P κ (λ). Acta Math. 186, 271–300 (2001)
Holz M., Steffens K., Weitz E.: Introduction to Cardinal Arithmetic. Birkhäuser, Basel (1999)
Matet P.: Game ideals. Ann. Pure Appl. Log. 158, 23–39 (2009)
Matet P.: The Magidor function and diamond. J. Symb. Log. 76, 405–417 (2011)
Matet, P.: Non-saturation of the non-stationary ideal on P κ (λ) with λ of countable cofinality. Math. Log. Q. To appear
Shioya M.: Splitting \({\mathcal{P}_\kappa\lambda}\) into maximally many stationary sets. Israel J. Math. 114, 347–357 (1999)
Solovay R.M.: Real-valued measurable cardinals. In: Scott, D.S. (eds) Axiomatic Set Theory, Proceedings of Symposia in Pure Mathematics vol. 13, Part 1, pp. 397–428. American Mathematical Society, Providence, RI (1971)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Matet, P. Non-saturation of the nonstationary ideal on P κ (λ) in case κ ≤ cf (λ) < λ. Arch. Math. Logic 51, 425–432 (2012). https://doi.org/10.1007/s00153-012-0270-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00153-012-0270-2