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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Existentially complete abelian lattice-ordered groups


Authors: A. M. W. Glass and Keith R. Pierce
Journal: Trans. Amer. Math. Soc. 261 (1980), 255-270
MSC: Primary 03C60; Secondary 03C35, 06F20
DOI: https://doi.org/10.1090/S0002-9947-1980-0576874-2
MathSciNet review: 576874
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Abstract: The theory of abelian totally ordered groups has a model completion. We show that the theory of abelian lattice-ordered groups has no model companion. Indeed, the Archimedean property can be captured by a first order $ \forall\exists\forall$ sentence for existentially complete abelian lattice-ordered groups, and distinguishes between finitely generic abelian lattice-ordered groups and infinitely generic ones. We then construct (by sheaf techniques) the model companions of certain classes of discrete abelian lattice-ordered groups.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1980-0576874-2
Keywords: Abelian lattice-ordered groups, model companion, model completion, existentially complete, algebraically closed, finite forcing, infinite forcing, sheaf, section
Article copyright: © Copyright 1980 American Mathematical Society