On the strong cell decomposition property for weakly o‐minimal structures |
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Authors: | Roman Wencel |
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Institution: | Instytut Matematyczny, Uniwersytetu Wroc?awskiego, , 50‐384 Wroc?aw, Poland |
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Abstract: | We consider a class of weakly o‐minimal structures admitting an o‐minimal style cell decomposition, for which one can construct certain canonical o‐minimal extension. The paper contains several fundamental facts concerning the structures in question. 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. |
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Keywords: | weak o‐minimality cell decomposition 03C64 |
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