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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


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.
  • V. A. Buevich, A variant of the proof of a completeness criterion for functions of $k$-valued logic, Diskret. Mat. 8 (1996), no. 4, 11–36 (Russian, with Russian summary); English transl., Discrete Math. Appl. 6 (1996), no. 5, 505–530. MR 1447318, DOI 10.1515/dma.1996.6.5.505
  • G. P. Gavrilov, Certain conditions for completeness in countable-valued logic, Dokl. Akad. Nauk SSSR 128 (1959), 21–24 (Russian). MR 0107602
  • G. P. Gavrilov, On functional completeness in countably-valued logic, Problemy Kibernet. No. 15 (1965), 5–64 (Russian). MR 0229511
  • Martin Goldstern and Saharon Shelah, Clones on regular cardinals, Fund. Math. 173 (2002), no. 1, 1–20. MR 1899044, DOI 10.4064/fm173-1-1
  • Martin Goldstern and Saharon Shelah. Large Intervals in the Clone Lattice. Algebra Universalis, 200x. math.RA/0208066.
  • Lutz Heindorf, The maximal clones on countable sets that include all permutations, Algebra Universalis 48 (2002), no. 2, 209–222. MR 1929905, DOI 10.1007/PL00012450
  • H. Machida and I. G. Rosenberg, A “large” essentially minimal clone over an infinite set, Proceedings of the International Conference on Algebra, Part 3 (Novosibirsk, 1989) Contemp. Math., vol. 131, Amer. Math. Soc., Providence, RI, 1992, pp. 159–167. MR 1175881
  • R. Pöschel and L. A. Kalužnin, Funktionen- und Relationenalgebren, Mathematische Monographien [Mathematical Monographs], vol. 15, VEB Deutscher Verlag der Wissenschaften, Berlin, 1979 (German). Ein Kapitel der diskreten Mathematik. [A chapter in discrete mathematics]. MR 543839
  • R. W. Quackenbush, A new proof of Rosenberg’s primal algebra characterization theorem, Finite algebra and multiple-valued logic (Szeged, 1979) Colloq. Math. Soc. János Bolyai, vol. 28, North-Holland, Amsterdam-New York, 1981, pp. 603–634. MR 648636
  • Ivo Rosenberg, Über die funktionale Vollständigkeit in den mehrwertigen Logiken. Struktur der Funktionen von mehreren Veränderlichen auf endlichen Mengen, Rozpravy Československé Akad. Věd Řada Mat. Přírod. Věd 80 (1970), no. 4, 93 (German). MR 0292647
  • I. G. Rosenberg, Some maximal closed classes of operations on infinite sets, Math. Ann. 212 (1974/75), 157–164. MR 351964, DOI 10.1007/BF01350783
  • I. G. Rosenberg, The set of maximal closed classes of operations on an infinite set $A$ has cardinality $2^{2{}^{\mid }{}^{A\mid }}$, Arch. Math. (Basel) 27 (1976), no. 6, 561–568. MR 429700, DOI 10.1007/BF01224718
  • Ivo G. Rosenberg and Dietmar Schweigert, Locally maximal clones, Elektron. Informationsverarb. Kybernet. 18 (1982), no. 7-8, 389–401 (English, with German and Russian summaries). MR 703778
  • Andrzej Rosłanowski and Saharon Shelah, Norms on possibilities. I. Forcing with trees and creatures, Mem. Amer. Math. Soc. 141 (1999), no. 671, xii+167. MR 1613600, DOI 10.1090/memo/0671
  • Saharon Shelah, On cardinal invariants of the continuum, Axiomatic set theory (Boulder, Colo., 1983) Contemp. Math., vol. 31, Amer. Math. Soc., Providence, RI, 1984, pp. 183–207. MR 763901, DOI 10.1090/conm/031/763901
  • Ágnes Szendrei, Clones in universal algebra, Séminaire de Mathématiques Supérieures [Seminar on Higher Mathematics], vol. 99, Presses de l’Université de Montréal, Montreal, QC, 1986. MR 859550
  • Eric K. van Douwen, The integers and topology, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 111–167. MR 776622
  • Jan van Mill and George M. Reed (eds.), Open problems in topology, North-Holland Publishing Co., Amsterdam, 1990. MR 1078636
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Additional Information
  • Martin Goldstern
  • Affiliation: Institute of Discrete Mathematics and Geometry, Vienna University of Technology, A-1040 Vienna, Austria
  • Email:
  • 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:
  • 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
  • © Copyright 2004 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 357 (2005), 3525-3551
  • MSC (2000): Primary 08A40; Secondary 03E50, 03E75
  • DOI:
  • MathSciNet review: 2146637