SOME UNUSUAL EPICOMPLETE ARCHIMEDEAN LATTICE-ORDERED GROUPS

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.