New axioms for the lattice-ordered groups existentially closed in W

Let W+ be the class of nonzero Archimedean lattice-ordered groups with distinguished strong order unit, viewed as structures for the first-order language {+, -, & BOTTOM;, & PROVES;, 0, 1}. This paper gives new axioms for the lattice-ordered groups existentially closed in W+ and uses them to show that (C(X), 1X) is existentially closed in W+ if and only if X is nonempty, pseudocompact, an almost -P-space, and a strongly zero-dimensional F-space with no isolated points.