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Preprint Number 708

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708. Will Johnson
A pathological o-minimal quotient
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Submission date: 11 April 2014.

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.

Mathematics Subject Classification: 03C64

Keywords and phrases:

Full text arXiv 1404.3175: pdf, ps.


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