Non-directed Archimedean ordered vector spaces of dimension >1 lack reflectors in the categories of Dedekind complete and universally complete vector lattices, so no free Dedekind complete vector lattices exist over sets with more than one generator.
Solovay,New proof of a theorem of Gaifman and Hales, Bull
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
fields
math.FA 1years
2026 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
The Dedekind completion of an Archimedean ordered vector space as a reflector
Non-directed Archimedean ordered vector spaces of dimension >1 lack reflectors in the categories of Dedekind complete and universally complete vector lattices, so no free Dedekind complete vector lattices exist over sets with more than one generator.