一个病态的o-最小商
A pathological o-minimal quotient
摘要：
我们给出了一个例子，一个可定义的商在一个O-最小的结构，不能消除任何一组参数，给出一个否定的答案Eleftheriou，Peterzil，和Ramakrishnan的问题。等价地，存在一个O-极小结构M，它的基本图不消除矩阵。我们也给出了一个积极的回答相关的问题，表明任何虚的O-最小结构是interdefinable超过一个独立集的参数与元组的实元素。这可以解释为可解释的集合看起来“局部”像可定义的集合，在某种意义上可以精确。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
