English

On defining irreducibility

Logic 2009-10-31 v1 Algebraic Geometry

Abstract

We show that irreducibility is not a first-order definable property of real algebraic varieties. The proof is based on the recent o-minimality result for the exponential function. We conjecture that irreducibility is not a definable property of complex algebraic varieties.

Keywords

Cite

@article{arxiv.math/9907002,
  title  = {On defining irreducibility},
  author = {Pascal Koiran},
  journal= {arXiv preprint arXiv:math/9907002},
  year   = {2009}
}