$C(\beta\mathbb{N}\setminus\mathbb{N})$ among the Archimedean $\ell$-groups with strong unit

Abstract

Let $\mathcal{W}^{+}$ be the class of Archimedean lattice-ordered groups with distinguished strong unit $1 \gt 0$. This paper studies the $\ell$-groups existentially closed (e.c.) in $\mathcal{W}^{+}$ and those infinitely generic (i.g.) in $\mathcal{W}^{+