Universality of the lattice of transformation monoids
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- by Michael Pinsker and Saharon Shelah PDF
- Proc. Amer. Math. Soc. 141 (2013), 3005-3011 Request permission
Abstract:
The set of all transformation monoids on a fixed set of infinite cardinality $\lambda$, equipped with the order of inclusion, forms a complete algebraic lattice $\operatorname {Mon}(\lambda )$ with $2^\lambda$ compact elements. We show that this lattice is universal with respect to closed sublattices; i.e., the closed sublattices of $\operatorname {Mon}(\lambda )$ are, up to isomorphism, precisely the complete algebraic lattices with at most $2^\lambda$ compact elements.References
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Additional Information
- Michael Pinsker
- Affiliation: Équipe de Logique Mathématique, Université Diderot – Paris 7, UFR de Mathématiques, 75205 Paris Cedex 13, France
- MR Author ID: 742015
- ORCID: 0000-0002-4727-918X
- Email: marula@gmx.at
- Saharon Shelah
- Affiliation: Institute of Mathematics, The 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: shelah@math.huji.ac.il
- Received by editor(s): June 24, 2011
- Received by editor(s) in revised form: September 3, 2011, September 12, 2011, and November 24, 2011
- Published electronically: May 21, 2013
- Additional Notes: The research of the first author was supported by an APART fellowship of the Austrian Academy of Sciences
The research of the second author was supported by German-Israeli Foundation for Scientific Research & Development Grant No. 963-98.6/2007.
The authors would like to thank an anonymous referee for valuable comments which led to significant improvements in the presentation of the paper. - Communicated by: Julia Knight
- © Copyright 2013 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 141 (2013), 3005-3011
- MSC (2010): Primary 06B15; Secondary 06B23, 20M20
- DOI: https://doi.org/10.1090/S0002-9939-2013-11566-2
- MathSciNet review: 3068953