On defining irreducibility

DOI10.1016/S0764-4442(00)00240-8zbMATH Open0954.03037arXivmath/9907002OpenAlexW3100612548MaRDI QIDQ4489997

Pascal Koiran

Publication date: 12 October 2000

Published in: Comptes Rendus de l'Académie des Sciences - Series I - Mathematics (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/math/9907002

zbMATH Keywords

semialgebraic seto-minimalityirreducible variety

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Real algebraic and real-analytic geometry (14P99) Model theory of ordered structures; o-minimality (03C64)

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