A pathological o-minimal quotient

Will Johnson

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arXiv · 1404.3175

A pathological o-minimal quotient

Will Johnson

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Abstract

We give an example of a definable quotient in an o-minimal structure which cannot be eliminated over any set of parameters, giving a negative answer to a question of Eleftheriou, Peterzil, and Ramakrishnan. Equivalently, there is an o-minimal structure M whose elementary diagram does not eliminate imaginaries. We also give a positive answer to a related question, showing that any imaginary in an o-minimal structure is interdefinable over an independent set of parameters with a tuple of real elements. This can be interpreted as saying that interpretable sets look "locally" like definable sets, in a sense which can be made precise.

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Will Johnson. 2014-04-11. A pathological o-minimal quotient. https://arxiv.org/abs/1404.3175

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