Abstract
A special map, called “contraction”, on ordered abelian groups is studied. A contraction contracts every archimedean class ≠ (0) to a set (a, -a) of two points. A weakly o-minimal theory of divisible ordered abelian groups with surjective contraction is given. It is shown not to have the algebraic exchange property. Contractions appear in a natural way in the theory of nonarchimedean exponential fields.
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© 1995 Springer Science+Business Media Dordrecht
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Kuhlmann, FV. (1995). Abelian Groups with Contractions II: Weak O-Minimality. In: Facchini, A., Menini, C. (eds) Abelian Groups and Modules. Mathematics and Its Applications, vol 343. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0443-2_27
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DOI: https://doi.org/10.1007/978-94-011-0443-2_27
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4198-0
Online ISBN: 978-94-011-0443-2
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