On Tameness, Measurability and the Independence Property
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911029270675456 |
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| author | Krapp, Lothar Sebastian Vermeil, Matthieu Wirth, Laura |
| author_facet | Krapp, Lothar Sebastian Vermeil, Matthieu Wirth, Laura |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08733 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Tameness, Measurability and the Independence Property Krapp, Lothar Sebastian Vermeil, Matthieu Wirth, Laura Logic Primary 03C64, 28A05, Secondary 12L12, 12J15, 03C40, 03C45, 54H05 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. |
| title | On Tameness, Measurability and the Independence Property |
| topic | Logic Primary 03C64, 28A05, Secondary 12L12, 12J15, 03C40, 03C45, 54H05 |
| url | https://arxiv.org/abs/2506.08733 |