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