1991
DOI: 10.2307/2274920
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The elementary class of products of totally ordered abelian group

Abstract: A basic goal in model-theoretic algebra is to obtain the classification of the complete extensions of a given (first-order) algebraic theory.Results of this type, for the theory of totally ordered abelian groups, were obtained first by A. Robinson and E. Zakon [5] in 1960, later extended by Yu. Gurevich [4] in 1964, and further clarified by P. Schmitt in [6].Within this circle of ideas, we give in this paper an axiomatization of the first-order theory of the class of all direct products of totally ordered abel… Show more

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Cited by 2 publications
(3 citation statements)
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“…If G is <*-dense, then from Proposition 1. 6 PROOF, (i) is immediate from Weispfenning's results in [15] and [17]. (ii) From Proposition 1.6, we have that G e r(/,(L,) i€/ ) for some family (Li) i6/ with Th((L() ie/ ) complete.…”
Section: \Di -9i\mentioning
confidence: 84%
See 1 more Smart Citation
“…If G is <*-dense, then from Proposition 1. 6 PROOF, (i) is immediate from Weispfenning's results in [15] and [17]. (ii) From Proposition 1.6, we have that G e r(/,(L,) i€/ ) for some family (Li) i6/ with Th((L() ie/ ) complete.…”
Section: \Di -9i\mentioning
confidence: 84%
“…(2) In [6] one of the authors gave a characterization of the elementary class of /-groups generated by the direct products of o-groups. From Theorem 3.2 it follows that, for the hyper-regular case, that characterization can be considerably simplified and extended to the elementary class generated by the direct sums of o-groups.…”
Section: Gji))mentioning
confidence: 99%
“…In [5], the author gave such a characterization for the abelian lattice-ordered groups (!-groups) considered as subdirect products of totally ordered groups (a superclass of the subdirectly irreducible ones). Using similar methods we will generalize this result and give some examples.…”
Section: Introductionmentioning
confidence: 99%