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Construction of existentially closed Abelian lattice-ordered groups using upper extensions

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The upper extension construction of Ball, Conrad, and Darnel is used to produce new examples of non-Archimedean existentially closed Abelian lattice-ordered groups and boundedly existentially closed Abelian lattice-ordered groups. Also… Click to show full abstract

The upper extension construction of Ball, Conrad, and Darnel is used to produce new examples of non-Archimedean existentially closed Abelian lattice-ordered groups and boundedly existentially closed Abelian lattice-ordered groups. Also given are conditions under which an upper extension of a projectable Abelian lattice-ordered group is projectable.

Keywords: existentially closed; lattice ordered; abelian lattice; ordered groups; closed abelian

Journal Title: Algebra universalis
Year Published: 2018

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