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Transactions of the American Mathematical Society

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Clones from creatures

Authors: Martin Goldstern and Saharon Shelah
Journal: Trans. Amer. Math. Soc. 357 (2005), 3525-3551
MSC (2000): Primary 08A40; Secondary 03E50, 03E75
Published electronically: November 4, 2004
MathSciNet review: 2146637
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Abstract | References | Similar Articles | Additional Information

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

Saharon Shelah
Affiliation: Institute of Mathematics, Hebrew University of Jerusalem, 91904 Jerusalem, Israel – and – Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08854

Keywords: Precomplete clones, maximal clones, clones on infinite sets, creature forcing, continuum hypothesis
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
Article copyright: © Copyright 2004 American Mathematical Society