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New axioms for the lattice-ordered groups existentially closed in

Volume 263 / 2023

Brian Wynne Fundamenta Mathematicae 263 (2023), 91-104 MSC: Primary 03C60; Secondary 06F20. DOI: 10.4064/fm280-6-2023 Published online: 29 August 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.

Authors

  • Brian WynneDepartment of Mathematics
    Lehman College, CUNY
    Gillet Hall, Room 211
    250 Bedford Park Blvd West
    Bronx, NY 10468, USA
    e-mail

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