The order and regular hulls of Riesz spaces (Q1920840)

We introduce the concept of order hull for a Riesz space (= a vector lattice). This, in particular, makes it possible to exhibit a simple realization of the Dedekind completion of an Archimedean Riesz space. We point out that in similar way the order completion of a Boolean algebra was implemented in [\textit{H. Gonsher}, Lect. Notes Math. 369, 60-70 (1974; Zbl 0276.54045)]. Together with the order hulls, we consider the regular hulls, i.e. the nonstandard hulls of Riesz spaces. The basic method for research in the present article is an embedding of some superstructure \(M\) containing the mathematical objects under study (Riesz spaces, and the like) into the Robinson nonstandard enlargement \({^*M}\). Moreover, we assume the embedding \(M\overset {*} \hookrightarrow{^*M}\) to be polysaturated, which allows us to apply the general saturation principle. The polysaturation assumption can be weakened in each concrete case. However, we refrain from doing so in order to avoid overloading the exposition with unnecessary details.