EXPANSIONS OF THE REAL FIELD BY OPEN SETS: DEFINABILITY VERSUS INTERPRETABILITY

Harvey Friedman (1) , Krzysztof Kurdyka (2) , Chris Miller (3) , Patrick Speissegger (4)

1 Department of Mathematics
2 LAMA - Laboratoire de Mathématiques
3 Department of Mathematics
4 Department of Mathematics & Statistics [Halmiton]

We produce an example of a Cantor set K such that for any definable map (in an o-minimal structure exponentially bounded) in k variables the image of the k-th cartesian power of K is nowhere dense. Then we give some consequences for the descriptive set theory.

Mots clés: expansion of the real field; o-minimal; projective hierarchy; Cantor set; Hausdorff dimension; Minkowski dimension.; Minkowski dimension

Domaines: Topologie géométrique [math.GT]

Harvey Friedman, Krzysztof Kurdyka, Chris Miller, Patrick Speissegger. EXPANSIONS OF THE REAL FIELD BY OPEN SETS: DEFINABILITY VERSUS INTERPRETABILITY. 2008. ⟨hal-00389216⟩