Definability of Geometric Properties in Algebraically Closed Fields

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Mathematical Logic Quarterly 45 (4):533-550 (1999)
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Abstract

We prove that there exists no sentence F of the language of rings with an extra binary predicat I2 satisfying the following property: for every definable set X ⊆ ℂ2, X is connected if and only if ⊧ F, where I2 is interpreted by X. We conjecture that the same result holds for closed subset of ℂ2. We prove some results motivated by this conjecture

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10.1002/malq.19990450411

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References found in this work

Model theory.Wilfrid Hodges - 2008 - Stanford Encyclopedia of Philosophy.
¹1-formulae on finite structures.M. Ajtai - 1983 - Annals of Pure and Applied Logic 24 (1):1.

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