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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

All creatures great and small


Authors: Martin Goldstern and Saharon Shelah
Journal: Trans. Amer. Math. Soc. 368 (2016), 7551-7577
MSC (2010): Primary 08A40; Secondary 03E40, 03E50, 03E75
DOI: https://doi.org/10.1090/tran/6568
Published electronically: February 29, 2016
MathSciNet review: 3546775
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Abstract: 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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Martin Goldstern
Affiliation: Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstraße 8–10/104, 1040 Wien, Austria
Email: martin.goldstern@tuwien.ac.at

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
Email: shelah@math.huji.ac.il

DOI: https://doi.org/10.1090/tran/6568
Keywords: Precomplete clones, maximal clones, clones on infinite sets, creature forcing, large creatures, cardinal arithmetic
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
Article copyright: © Copyright 2016 American Mathematical Society