## Existentially complete abelian lattice-ordered groups

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- by A. M. W. Glass and Keith R. Pierce
- Trans. Amer. Math. Soc.
**261**(1980), 255-270 - DOI: https://doi.org/10.1090/S0002-9947-1980-0576874-2
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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.## References

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## Bibliographic Information

- © Copyright 1980 American Mathematical Society
- 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