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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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Strongly almost disjoint sets and weakly uniform bases
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by Z. T. Balogh, S. W. Davis, W. Just, S. Shelah and P. J. Szeptycki PDF
Trans. Amer. Math. Soc. 352 (2000), 4971-4987 Request permission

Abstract:

A combinatorial principle CECA is formulated and its equivalence with GCH + certain weakenings of $\Box _\lambda$ for singular $\lambda$ is proved. CECA is used to show that certain “almost point-$<\tau$” families can be refined to point-$< \tau$ families by removing a small set from each member of the family. This theorem in turn is used to show the consistency of “every first countable $T_1$-space with a weakly uniform base has a point-countable base.”
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Additional Information
  • Z. T. Balogh
  • Affiliation: Department of Mathematics, Miami University, Oxford, Ohio 45056
  • Email: ztbalogh@miavx1.acs.muohio.edu
  • S. W. Davis
  • Affiliation: Department of Mathematics, Miami University, Oxford, Ohio 45056
  • Email: swdavis@miavx1.muohio.edu
  • W. Just
  • Affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701
  • Email: just@math.ohiou.edu
  • S. Shelah
  • Affiliation: Institute of Mathematics, The Hebrew University, Givat Ram, 91904 Jerusalem, Israel
  • MR Author ID: 160185
  • ORCID: 0000-0003-0462-3152
  • Email: shelah@math.huji.ac.il
  • P. J. Szeptycki
  • Affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701
  • Email: szeptyck@math.ohiou.edu
  • Received by editor(s): March 17, 1998
  • Published electronically: June 20, 2000
  • Additional Notes: The first author’s research was partially supported by NSF grant DMS-9623391. The third author’s research was done during visits at Rutgers University and The Hebrew University, Jerusalem, which were supported by NSF grant DMS-9704477 and the Landau Center. The fourth author was partially supported by the Israel Basic Research Fund. This is publication number 674 in Shelah’s publication list.
  • © Copyright 2000 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 352 (2000), 4971-4987
  • MSC (2000): Primary 03E05, 03E35, 03E75, 54D70
  • DOI: https://doi.org/10.1090/S0002-9947-00-02599-X
  • MathSciNet review: 1707497