Quantifier elimination in ordered abelian groups
Confluentes Mathematici, Volume 3 (2011) no. 4, pp. 587-615.

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 linear on finitely many definable pieces.

Published online:
DOI: 10.1142/S1793744211000473
Raf Cluckers 1; Immanuel Halupczok 1

1
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Raf Cluckers; Immanuel Halupczok. Quantifier elimination in ordered abelian groups. Confluentes Mathematici, Volume 3 (2011) no. 4, pp. 587-615. doi : 10.1142/S1793744211000473. https://cml.centre-mersenne.org/articles/10.1142/S1793744211000473/

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