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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Cofinality of the nonstationary ideal
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by Pierre Matet, Andrzej Rosłanowski and Saharon Shelah PDF
Trans. Amer. Math. Soc. 357 (2005), 4813-4837 Request permission


We show that the reduced cofinality of the nonstationary ideal ${\mathcal N\! S}_\kappa$ on a regular uncountable cardinal $\kappa$ may be less than its cofinality, where the reduced cofinality of ${\mathcal N\! S}_\kappa$ is the least cardinality of any family ${\mathcal F}$ of nonstationary subsets of $\kappa$ such that every nonstationary subset of $\kappa$ can be covered by less than $\kappa$ many members of ${\mathcal F}$. For this we investigate connections of the various cofinalities of ${\mathcal N\! S}_\kappa$ with other cardinal characteristics of ${}^{\textstyle \kappa }\kappa$ and we also give a property of forcing notions (called manageability) which is preserved in ${<}\kappa$–support iterations and which implies that the forcing notion preserves non-meagerness of subsets of ${}^{\textstyle \kappa }\kappa$ (and does not collapse cardinals nor changes cofinalities).
  • Yoshihiro Abe, A hierarchy of filters smaller than $\textrm {CF}_{\kappa \lambda }$, Arch. Math. Logic 36 (1997), no. 6, 385–397. MR 1477763, DOI 10.1007/s001530050071
  • Bohuslav Balcar and Petr Simon, Disjoint refinement, Handbook of Boolean algebras, Vol. 2, North-Holland, Amsterdam, 1989, pp. 333–388. MR 991597
  • James Cummings and Saharon Shelah, Cardinal invariants above the continuum, Ann. Pure Appl. Logic 75 (1995), no. 3, 251–268. MR 1355135, DOI 10.1016/0168-0072(95)00003-Y
  • Moti Gitik, The negation of the singular cardinal hypothesis from $o(\kappa )=\kappa ^{++}$, Ann. Pure Appl. Logic 43 (1989), no. 3, 209–234. MR 1007865, DOI 10.1016/0168-0072(89)90069-9
  • Moti Gitik and Carmi Merimovich, Possible values for $2^{\aleph _n}$ and $2^{\aleph _\omega }$, Ann. Pure Appl. Logic 90 (1997), no. 1-3, 193–241. MR 1489309, DOI 10.1016/S0168-0072(97)00037-7
  • Thomas Jech, Set theory, Pure and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 506523
  • Avner Landver. Singular Baire numbers and related topics. Ph.D. thesis, University of Wisconsin, Madison, 1990.
  • Menachem Magidor, On the singular cardinals problem. I, Israel J. Math. 28 (1977), no. 1-2, 1–31. MR 491183, DOI 10.1007/BF02759779
  • Pierre Matet and Janusz Pawlikowski, $Q$-pointness, $P$-pointness and feebleness of ideals, J. Symbolic Logic 68 (2003), no. 1, 235–261. MR 1959318, DOI 10.2178/jsl/1045861512
  • Pierre Matet, Cédric Péan, and Saharon Shelah. Cofinality of normal ideals on $P_\kappa (\lambda )$, I. Archive for Mathematical Logic. math.LO/0404318.
  • Pierre Matet, Cédric Péan, and Saharon Shelah. Cofinality of normal ideals on $P_\kappa (\lambda )$, II. Israel Journal of Mathematics, to appear.
  • Carmi Merimovich, Extender-based Radin forcing, Trans. Amer. Math. Soc. 355 (2003), no. 5, 1729–1772. MR 1953523, DOI 10.1090/S0002-9947-03-03202-1
  • Miri Segal. Master Thesis. The Hebrew University of Jerusalem, 1996. Menachem Magidor, adviser.
  • S. Shelah, A weak generalization of MA to higher cardinals, Israel J. Math. 30 (1978), no. 4, 297–306. MR 505492, DOI 10.1007/BF02761994
  • S. Shelah, Strong partition relations below the power set: consistency; was Sierpiński right? II, Sets, graphs and numbers (Budapest, 1991) Colloq. Math. Soc. János Bolyai, vol. 60, North-Holland, Amsterdam, 1992, pp. 637–668. MR 1218224
  • Saharon Shelah, Was Sierpiński right? IV, J. Symbolic Logic 65 (2000), no. 3, 1031–1054. MR 1791363, DOI 10.2307/2586687
  • Saharon Shelah and Lee Stanley. Generalized Martin’s axiom and Souslin’s hypothesis for higher cardinals. Israel Journal of Mathematics, 43:225–236, 1982. Corrections in [Sh:154a].
  • Saharon Shelah and Lee Stanley. Corrigendum to: “Generalized Martin’s axiom and Souslin’s hypothesis for higher cardinals” [Israel Journal of Mathematics 43 (1982), no. 3, 225–236; MR 84h:03120]. Israel Journal of Mathematics, 53:304–314, 1986.
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Additional Information
  • Pierre Matet
  • Affiliation: Departement de Mathématiques, Université de Caen – CNRS, BP 5186, 14032 Caen Cedex, France
  • Email:
  • Andrzej Rosłanowski
  • Affiliation: Department of Mathematics, University of Nebraska at Omaha, Omaha, Nebraska 68182-0243
  • MR Author ID: 288334
  • Email:
  • Saharon Shelah
  • Affiliation: Institute of Mathematics, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel – and – Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08854
  • MR Author ID: 160185
  • ORCID: 0000-0003-0462-3152
  • Email:
  • Received by editor(s): March 3, 2003
  • Published electronically: June 29, 2005
  • Additional Notes: The second author thanks the University Committee on Research of the University of Nebraska at Omaha for partial support. He also thanks his wife, Małgorzata Jankowiak–Rosłanowska, for supporting him when he was preparing the final version of this paper.
    The research of the third author was partially supported by the Israel Science Foundation. Publication 799
  • © Copyright 2005 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 357 (2005), 4813-4837
  • MSC (2000): Primary 03E05, 03E35, 03E55
  • DOI:
  • MathSciNet review: 2165389