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The structure on the real field generated by the standard part map on an
ominimal expansion of a real closed field  Jana Maříková
;  Date: 
1 Jun 2007  Abstract:  Let R be a sufficiently saturated ominimal expansion of a real closed field,
let O be the convex hull of the rationals in R, and let st: O^n o
mathbb{R}^n be the standard part map. For X subseteq R^n define st(X):=st(X
cap O^n). We let mathbb{R}_{ind} be the structure with underlying set
mathbb{R} and expanded by all sets of the form st(X), where X subseteq R^{n}
is definable in R and n=1,2,.... We show that the subsets of mathbb{R}^n that
are definable in mathbb{R}_{ind} are exactly the finite unions of sets of the
form st(X) setminus st(Y), where X,Y subseteq R^n are definable in R. A
consequence of the proof is a partial answer to a question by Hrushovski,
Peterzil and Pillay about the existence of measures with certain invariance
properties on the lattice of bounded definable sets in R^n.  Source:  arXiv, arxiv.0706.0182  Services:  Forum  Review  PDF  Favorites 


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