# Sh:577

- Gitik, M., & Shelah, S. (1997).
*Less saturated ideals*. Proc. Amer. Math. Soc.,**125**(5), 1523–1530. arXiv: math/9503203 DOI: 10.1090/S0002-9939-97-03702-7 MR: 1363421 -
Abstract:

We prove the following:(1) If \kappa is weakly inaccessible then NS_\kappa is not \kappa^+-saturated.

(2) If \kappa is weakly inaccessible and \theta<\kappa is regular then NS^\theta_\kappa is not \kappa^+-saturated.

(3) If \kappa is singular then NS^{cf(\kappa)}_{\kappa^+} is not \kappa^{++}-saturated.

Combining this with previous results of Shelah, one obtains the following: (A) If \kappa>\aleph_1 then NS_\kappa is not \kappa^+-saturated. (B) If \theta^+<\kappa then NS^\theta_\kappa is not \kappa^+-saturated.

- published version (8p)

Bib entry

@article{Sh:577, author = {Gitik, Moti and Shelah, Saharon}, title = {{Less saturated ideals}}, journal = {Proc. Amer. Math. Soc.}, fjournal = {Proceedings of the American Mathematical Society}, volume = {125}, number = {5}, year = {1997}, pages = {1523--1530}, issn = {0002-9939}, doi = {10.1090/S0002-9939-97-03702-7}, mrclass = {03E55 (03E05 03E35)}, mrnumber = {1363421}, mrreviewer = {Carlos A. Di Prisco}, doi = {10.1090/S0002-9939-97-03702-7}, note = {\href{https://arxiv.org/abs/math/9503203}{arXiv: math/9503203}}, arxiv_number = {math/9503203} }