Submission date: 20 February 2012.

Abstract:

The paper contains several fundamental results concerning weakly o-minimal structures with the strong cell decomposition property. Among other things, it is proved that the strong cell decomposition property is preserved under elementary equivalences. We also investigate fiberwise properties (of definable sets and definable functions), definable equivalence relations and conditions implying elimination of imaginaries.

Mathematics Subject Classification: 03C64

Keywords and phrases: weak o-minimality, cell decomposition

Full text: pdf, dvi, ps.