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Riesz spaces and the ultrafilter theorem. I. (English) Zbl 0781.46009

In this attractive paper the authors show among others that the Kakutani representation theorem for order unit spaces is equivalent to the ultrafilter theorem and that of Lipecki-Luxemburg-Schep theorem is equivalent to the Hahn-Banach theorem for Riesz homomorphisms. Various other equivalents of this kind are considered.

MSC:

46A40 Ordered topological linear spaces, vector lattices
06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
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