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The theorem of the complement for nested sub-Pfaffian sets. (English) Zbl 1226.14075

The authors prove a very important theorem about the complement of nested sub-Pfaffian sets. More precisely, the basic objects of their study are nested Pfaffian sets over a given \(o\)-minimal expansion of the real field. A nested sub-Pfaffian set is the projection of a positive Boolean combination of definable sets and nested Rolle leaves. In this situation they prove that the complement is again a nested sub-Pfaffian set. In the opinion of the reviewer it would be very interesting to compare the presented proof with the one from his old paper entitled “On the Gabrielov theorem for subpfaffian sets” [in: Real analytic and algebraic geometry. Proceedings of the international conference, Trento, Italy, September 21-25, 1992. Berlin: Walter de Gruyter. 149–160 (1995; Zbl 0829.32003)].

MSC:

14P10 Semialgebraic sets and related spaces
58A17 Pfaffian systems
03C99 Model theory

Citations:

Zbl 0829.32003
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References:

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