Submission date: 4 January 2008.

Abstract:

In the paper we establish an o-minimal style cell decomposition (the strong cell decomposition property) for weakly o-minimal non-valuational expansions of ordered groups. This generalizes an analogous result of Macpherson, Marker and Steinhorn for weakly o-minimal non-valuational expansions of ordered fields. For weakly o-minimal structures with the strong cell decomposition property we construct a canonical o-minimal extension. Finally we make attempts towards generalizing the o-minimal Euler characteristics to the class of sets definable in weakly o-minimal structures with the strong cell decomposition property.

Mathematics Subject Classification: 03C64

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