New axioms for the lattice-ordered groups existentially closed in
Volume 263 / 2023
Abstract
Let \bf {W}^+ be the class of nonzero Archimedean lattice-ordered groups with distinguished strong order unit, viewed as structures for the first-order language \{ +, -, \wedge , \vee , 0, 1 \}. This paper gives new axioms for the lattice-ordered groups existentially closed in \bf {W}^+ and uses them to show that (C(X),1_X) is existentially closed in \bf {W}^+ if and only if X is nonempty, pseudocompact, an almost-P-space, and a strongly zero-dimensional F-space with no isolated points.