First-order theories of subgroups of divisible Hahn products

Annals of Pure and Applied Logic 121 (2-3):261-279 (2003)

Francesca Marie Lucas
Oxford Brookes University
Some first-order theories of divisible ℓ-groups are well known, for example the theory of the totally ordered ones and the theories of the projectable ones , Lattice-ordered Groups, Kluwer Academic Press, Dordrecht, 1989, pp. 41–79). In this paper we study some theories of nonprojectable divisible ℓ-groups, the simplest example of which is . We introduce a generalization of the projectability property . We prove that the class of r-projectable special-valued divisible ℓ-groups is an elementary class and give a classification of its completions
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DOI 10.1016/s0168-0072(02)00115-x
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