B-Minimality

@article{Cluckers2007BMinimality,
  title={B-Minimality},
  author={R. Cluckers and F. Loeser},
  journal={J. Math. Log.},
  year={2007},
  volume={7}
}
We introduce a new notion of tame geometry for structures admitting an abstract notion of balls. The notion is named b-minimality and is based on definable families of points and balls. We develop a dimension theory and prove a cell decomposition theorem for bminimal structures. We show that b-minimality applies to the theory of Henselian valued fields of characteristic zero, generalizing work by Denef–Pas [25, 26]. Structures which are o-minimal, v-minimal, or p-minimal and which satisfy some… Expand
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