Bounded countable atomic compactness of ordered groups

Friedrich Wehrung (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

We show that whenever $A$ is a monotone $\sigma$-complete dimension group, then $A^+\cup\{\infty\}$ is countably equationally compact, and we show how this property can supply the necessary amount of completeness in several kinds of problems. In particular, if $A$ is a countable dimension group and $E$ is a monotone $\sigma$-complete dimension group, then the ordered group of all relatively bounded homomorphisms from $A$ to $E$ is a monotone $\sigma$-complete dimension group.

Mots clés: equational compactness; Monotone $\sigma$-complete groups; dimension groups

Domaines: Mathématiques générales [math.GM]

Friedrich Wehrung. Bounded countable atomic compactness of ordered groups. Fundamenta Mathematicae, 1995, 148, pp.101-116. ⟨hal-00004657⟩