Strong theories of ordered abelian groups

2015/11/26 by Dolich, Alfred, Goodrick, John · 2 citations
#03C45 #03C64 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1511.08274

Abstract

We consider strong expansions of the theory of ordered abelian groups. We show that the assumption of strength has a multitude of desirable consequences for the structure of definable sets in such theories, in particular as relates to definable infinite discrete sets. We also provide a range of examples of strong expansions of ordered abelian groups which demonstrate the great variety of such theories.

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• Consequences of Dependent Dividing on Burden
• Dimension theory for the asymptotic couple of the field of logarithmic transseries

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