Some unusual epicomplete Archimedean lattice-ordered groups
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- by Anthony W. Hager PDF
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Abstract:
An Archimedean $l$-group is epicomplete if it is divisible and $\sigma$-complete, both laterally and conditionally. Under various circumstances it has been shown that epicompleteness implies the existence of a compatible reduced $f$-ring multiplication; the question has arisen whether or not this is always true. We show that a set-theoretic condition weaker than the continuum hypothesis implies โnotโ, and conjecture the converse. The examples also fail decent representation and existence of some other compatible operations.References
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Additional Information
- Anthony W. Hager
- Affiliation: Department of Mathematics and Computer Science, Wesleyan University, Middletown, Connecticut 06459
- Email: ahager@wesleyan.edu
- Received by editor(s): November 19, 2013
- Published electronically: January 14, 2015
- Communicated by: Ken Ono
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 1969-1980
- MSC (2010): Primary 06E20; Secondary 03E50, 06B15, 06F25, 08A99, 18A20, 18A40, 46E25, 54C30, 54G05
- DOI: https://doi.org/10.1090/S0002-9939-2015-12448-3
- MathSciNet review: 3314107