共查询到7条相似文献,搜索用时 46 毫秒
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Roman Wencel 《Mathematical Logic Quarterly》2012,58(6):449-467
Given a group (G, ·), G?Mm, definable in a first‐order structure $\mathcal {M}=(M,\ldots )Given a group (G, ·), G?Mm, definable in a first‐order structure $\mathcal {M}=(M,\ldots )$ equipped with a dimension function and a topology satisfying certain natural conditions, we find a large open definable subset V?G and define a new topology τ on G with which (G, ·) becomes a topological group. Moreover, τ restricted to V coincides with the topology of V inherited from Mm. Likewise we topologize transitive group actions and fields definable in $\mathcal {M}$. These results require a series of preparatory facts concerning dimension functions, some of which might be of independent interest. 相似文献
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Janusz Gwozdziewicz Krzysztof Kurdyka Adam Parusinski 《Proceedings of the American Mathematical Society》1999,127(4):1057-1064
We prove that every polynomial of degree has at most zeros on the curve . As a consequence we deduce that the existence of a uniform bound for the number of zeros of polynomials of a fixed degree on an analytic curve does not imply that this curve belongs to an o-minimal structure.
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Eva Leenknegt 《Mathematical Logic Quarterly》2012,58(6):482-497
We develop a notion of cell decomposition suitable for studying weak p‐adic structures (reducts of p‐adic fields where addition and multiplication are not (everywhere) definable). As an example, we consider a structure with restricted addition. 相似文献
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Roman Wencel 《Mathematical Logic Quarterly》2013,59(6):452-470
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. 相似文献
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Raf Cluckers 《Transactions of the American Mathematical Society》2004,356(4):1489-1499
We prove a conjecture of Denef on parameterized -adic analytic integrals using an analytic cell decomposition theorem, which we also prove in this paper. This cell decomposition theorem describes piecewise the valuation of analytic functions (and more generally of subanalytic functions), the pieces being geometrically simple sets, called cells. We also classify subanalytic sets up to subanalytic bijection.