Nonstandard hulls of vector lattices (Q1897966)

The author defines the nonstandard hull \(\overline E\) of a vector lattice \(E\) in an analogous way to the usual definition of the nonstandard hull \(\widetilde V\) of a normed vector space \(V\), whereas the absolute value on \(E\) replaces the role of the norm on \(V\). For a normed vector lattice \(E\), he compares \(\overline E\) and \(\widetilde E\). He also investigates a situation where \(E\) is lattice isomorphic to \(\overline E\) and calculates the nonstandard hull of several examples. The reviewer remarks that an alternative to the author's definition is offered via an ultrapower construction [the reviewer and \textit{A. C. M. van Rooij}, Compos. Math. 83, No. 3, 311-327 (1992; Zbl 0781.46009)]. In the latter alternative, the nonstandard hull of any Archimedean vector lattice is Archimedean, thus avoiding the question at the end of this paper.