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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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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Additional Information
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
MR Author ID:
160185
ORCID:
0000-0003-0462-3152
Email:
shelah@math.huji.ac.il
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
