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arXiv · 1110.3200

Quantifier elimination in ordered abelian groups

Raf Cluckers·Immanuel Halupczok
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Abstract

We give a new proof of quantifier elimination in the theory of all ordered abelian groups in a suitable language. More precisely, this is only "quantifier elimination relative to ordered sets" in the following sense. Each definable set in the group is a union of a family of quantifier free definable sets, where the parameter of the family runs over a set definable (with quantifiers) in a sort which carries the structure of an ordered set with some additional unary predicates. As a corollary, we find that all definable functions in ordered abelian groups are piecewise affine linear on finitely many definable pieces.

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Raf Cluckers, Immanuel Halupczok. 2011-10-14. Quantifier elimination in ordered abelian groups. https://doi.org/10.1142/s1793744211000473

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