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On the (non) superstable part of the free group. (English) Zbl 1432.03064

Summary: In this short note we prove that a definable set \(X\) over \(\mathbb{F}_n\) is superstable only if \(X(\mathbb{F}_n) = X(\mathbb{F}_\omega)\).

MSC:

03C60 Model-theoretic algebra
03C45 Classification theory, stability, and related concepts in model theory
20E05 Free nonabelian groups
20A15 Applications of logic to group theory
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References:

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