Abstract
Given an arbitrary o-minimal expansion of a real closed field R, we
develop the basic theory of definable manifolds and definable analytic sets, with
respect to the algebraic closure of R, along the lines of classical complex analytic
geometry. Because of the o-minimality assumption, we obtain strong theorems on
removal of singularities and strong finiteness results in both the classical and the
nonstandard settings.
We also use a theorem of Bianconi to characterize all complex analytic sets
definable in Rexp.
develop the basic theory of definable manifolds and definable analytic sets, with
respect to the algebraic closure of R, along the lines of classical complex analytic
geometry. Because of the o-minimality assumption, we obtain strong theorems on
removal of singularities and strong finiteness results in both the classical and the
nonstandard settings.
We also use a theorem of Bianconi to characterize all complex analytic sets
definable in Rexp.
| Original language | English |
|---|---|
| Title of host publication | Model Theory with Applications to Algebra and Analysis |
| Editors | Z. Chatzidakis , D. Macpherson , A. Pillay , A. Wilkie |
| Pages | 117-166 |
| State | Published - 2008 |