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First-order theories of subgroups of divisible Hahn products

✍ Scribed by F. Lucas

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 207 KB
Volume: 121
Category: Article
ISSN: 0168-0072
DOI: 10.1016/s0168-0072(02)00115-x

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✦ Synopsis

All the '-groups we consider are Abelian.) Some ÿrst-order theories of divisible '-groups are well known, for example the theory of the totally ordered ones and the theories of the projectable ones (in: A.M.W. Glass, W.C. Holland (Eds.), Lattice-ordered Groups, Kluwer Academic Press, Dordrecht, 1989, pp. 41-79). In this paper we study some theories of nonprojectable divisible '-groups, the simplest example of which is R ×(R × R) (the lexicographic product of R by the direct product R × R). We introduce a generalization of the projectability property (r-projectability). We prove that the class of r-projectable special-valued divisible '-groups is an elementary class and give a classiÿcation of its completions.

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