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On defining irreducibility

Pascal Koiran
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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.

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Pascal Koiran. 1999-07-01. On defining irreducibility. https://doi.org/10.1016/s0764-4442(00)00240-8

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