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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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Ultrafilters on $\omega$-their ideals and their cardinal characteristics
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by Saharon Shelah, Jörg Brendle and Saharon Shelah PDF
Trans. Amer. Math. Soc. 351 (1999), 2643-2674 Request permission


For a free ultrafilter $\mathcal {U}$ on $\omega$ we study several cardinal characteristics which describe part of the combinatorial structure of $\mathcal {U}$. We provide various consistency results; e.g. we show how to force simultaneously many characters and many $\pi$–characters. We also investigate two ideals on the Baire space $\omega ^{\omega }$ naturally related to $\mathcal {U}$ and calculate cardinal coefficients of these ideals in terms of cardinal characteristics of the underlying ultrafilter.
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Additional Information
  • Jörg Brendle
  • Affiliation: Department of Mathematics, Dartmouth College, Bradley Hall, Hanover, New Hampshire 03755
  • Address at time of publication: Graduate School of Science and Technology, Kobe University, Rokko–dai, Nada, Kobe 657-8501, Japan
  • Email:
  • Saharon Shelah
  • Affiliation: Institute of Mathematics, The Hebrew University, Jerusalem 91904, Israel; Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
  • Received by editor(s): March 10, 1997
  • Received by editor(s) in revised form: November 4, 1997
  • Published electronically: March 8, 1999
  • Additional Notes: The research of the first author was partially supported by DFG–grant Nr. Br 1420/1–1.
    The research of the second author was supported by the German–Israeli Foundation for Scientific Research & Development Grant No. G-294.081.06/93. Publication 642 on the second author’s list of publications.
  • © Copyright 1999 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 351 (1999), 2643-2674
  • MSC (1991): Primary 03E05, 03E35
  • DOI:
  • MathSciNet review: 1686797