## 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 |
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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 |