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Theoretical analysis reveals a real subfield defining a non-Lebesgue measurable set via first-order ring formulas, highlighting structural boundaries in model-theoretic tame geometry.
In the area of Tame Geometry, different model-theoretic tameness conditions are established and their relationships are analyzed. We construct a subfield K of the real numbers that lacks several such tameness properties. As our main result, we present a first-order formula in the language of rings defining a set in K that is not Lebesgue measurable. Moreover, K has the independence property and admits both archimedean and non-archimedean orderings.
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Krapp et al. (2026) studied this question.
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