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.
Relative Pfaffian closure for definably complete Baire structures / Fornasiero, Antongiulio; Servi, Tamara. - In: ILLINOIS JOURNAL OF MATHEMATICS. - ISSN 0019-2082. - STAMPA. - 55:(2011), pp. 1203-1219.
Relative Pfaffian closure for definably complete Baire structures
Fornasiero, Antongiulio;
2011
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.File | Dimensione | Formato | |
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euclid.ijm.1369841803.pdf
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