English

On Tameness, Measurability and the Independence Property

Logic 2025-07-01 v2

Abstract

In the area of Tame Geometry, different model-theoretic tameness conditions are established and their relationships are analyzed. We construct a subfield KK 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 KK. Moreover, KK has the independence property and admits both archimedean and non-archimedean orderings.

Keywords

Cite

@article{arxiv.2506.08733,
  title  = {On Tameness, Measurability and the Independence Property},
  author = {Lothar Sebastian Krapp and Matthieu Vermeil and Laura Wirth},
  journal= {arXiv preprint arXiv:2506.08733},
  year   = {2025}
}

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19 pages