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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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Clones from creatures
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by Martin Goldstern and Saharon Shelah PDF
Trans. Amer. Math. Soc. 357 (2005), 3525-3551 Request permission

Abstract:

We show that (consistently) there is a clone $\mathcal {C}$ on a countable set such that the interval of clones above $\mathcal {C}$ is linearly ordered and has no coatoms.
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Additional Information
  • Martin Goldstern
  • Affiliation: Institute of Discrete Mathematics and Geometry, Vienna University of Technology, A-1040 Vienna, Austria
  • Email: goldstern@tuwien.ac.at
  • Saharon Shelah
  • Affiliation: Institute of Mathematics, 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: shelah@math.huji.ac.il
  • Received by editor(s): March 7, 2003
  • Received by editor(s) in revised form: December 2, 2003
  • Published electronically: November 4, 2004
  • Additional Notes: The first author is grateful to the Department of Mathematics, Rutgers University, New Jersey, for their hospitality during a visit in September 2002
    The second author’s research was supported by the US-Israel Binational Science Foundation. Publication 808.
    A preprint of this paper is available at http://www.arXiv.org/math.RA/0212379/
  • © Copyright 2004 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 357 (2005), 3525-3551
  • MSC (2000): Primary 08A40; Secondary 03E50, 03E75
  • DOI: https://doi.org/10.1090/S0002-9947-04-03593-7
  • MathSciNet review: 2146637