Abstract
Speissegger proved that the Pfaffian closure of an o-minimal expansion of the real field is o-minimal. Here we give a first order version of this result: having introduced the notion of definably complete Baire structure, we define the relative Pfaffian closure of an o-minimal structure inside a definably complete Baire structure, and we prove its o-minimality. We derive effective bounds on some topological invariants of sets definable in the Pfaffian closure of an o-minimal expansion of the real field.
Citation
Antongiulio Fornasiero. Tamara Servi. "Relative Pfaffian closure for definably complete Baire structures." Illinois J. Math. 55 (3) 1203 - 1219, Fall 2011. https://doi.org/10.1215/ijm/1369841803
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