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arXiv · 2506.08733

On Tameness, Measurability and the Independence Property

Lothar Sebastian Krapp·Matthieu Vermeil·Laura Wirth
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Abstract

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 of such tameness properties. As our main result, we present a first-order formula in the language of rings that defines a non-Borel set in $K$. Moreover, $K$ has the independence property and admits both archimedean and non-archimedean orderings.

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Lothar Sebastian Krapp, Matthieu Vermeil, Laura Wirth. 2025-06-10. On Tameness, Measurability and the Independence Property. https://arxiv.org/abs/2506.08733

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