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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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by Martin Goldstern and Saharon Shelah PDF
Trans. Amer. Math. Soc. 368 (2016), 7551-7577 Request permission


Let $\lambda$ be an uncountable regular cardinal. Assuming $2^{[\lambda ]}=\lambda ^+$, we show that the clone lattice on a set of size $\lambda$ is not dually atomic.
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Additional Information
  • Martin Goldstern
  • Affiliation: Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstraße 8–10/104, 1040 Wien, Austria
  • Email:
  • Saharon Shelah
  • Affiliation: Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem, 91904, 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): August 21, 2012
  • Received by editor(s) in revised form: August 5, 2014
  • Published electronically: February 29, 2016
  • Additional Notes: The first author was supported by FWF grant P17627-N12. The second author was supported by the United States-Israel Binational Science Foundation, grant 2002323, publication 884
  • © Copyright 2016 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 368 (2016), 7551-7577
  • MSC (2010): Primary 08A40; Secondary 03E40, 03E50, 03E75
  • DOI:
  • MathSciNet review: 3546775