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Some unusual epicomplete Archimedean lattice-ordered groups


Author: Anthony W. Hager
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
Published electronically: January 14, 2015
MathSciNet review: 3314107
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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 ``not'', and conjecture the converse. The examples also fail decent representation and existence of some other compatible operations.


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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

DOI: https://doi.org/10.1090/S0002-9939-2015-12448-3
Keywords: Lattice-ordered group, $f$-ring, epicomplete, reflection, $\sigma$-complete, truncation, essential completion, continuum hypothesis, basically disconnected space
Received by editor(s): November 19, 2013
Published electronically: January 14, 2015
Communicated by: Ken Ono
Article copyright: © Copyright 2015 American Mathematical Society