Publications > Preprint server > Preprint Number 708
Preprint Number 708
708. Will Johnson
A pathological o-minimal quotient
Submission date: 11 April 2014.
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:
|Last updated: April 30 2014 02:46||Please send your corrections to:|