Duke Mathematical Journal
- Duke Math. J.
- Volume 155, Number 1 (2010), 35-90.
The theorem of the complement for nested sub-Pfaffian sets
Let be an o-minimal expansion of the real field, and let be the language consisting of all nested Rolle leaves over . We call a set nested sub-Pfaffian over if it is the projection of a positive Boolean combination of definable sets and nested Rolle leaves over . Assuming that admits analytic cell decomposition, we prove that the complement of a nested sub-Pfaffian set over is again a nested sub-Pfaffian set over . As a corollary, we obtain that if admits analytic cell decomposition, then the Pfaffian closure of is obtained by adding to all nested Rolle leaves over , a one-stage process, and that is model complete in the language .
Duke Math. J., Volume 155, Number 1 (2010), 35-90.
First available in Project Euclid: 23 September 2010
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Lion, Jean-Marie; Speissegger, Patrick. The theorem of the complement for nested sub-Pfaffian sets. Duke Math. J. 155 (2010), no. 1, 35--90. doi:10.1215/00127094-2010-050. https://projecteuclid.org/euclid.dmj/1285247218