MathDBShelah's conjecture for NIP real fields
Shelah's conjecture for NIP real fields
A real field is an ordered field in which every positive element has a square root and every odd-degree polynomial has a root. A theory, and hence a field in its language, is NIP if it does not have the independence property. A real field is almost real closed if it admits a henselian valuation with real closed residue field.
Shelah's conjecture for NIP real fields. Any NIP real field is almost real closed.
This is a real-field specialization of Shelah's conjecture on the classification of NIP fields. The source records it as a conjectural classification statement; its resolution is not specified here.
Sources & referencesView supporting material
Primary source
Lothar Sebastian Krapp, Matthieu Vermeil and Laura Wirth, “On Tameness, Measurability and the Independence Property”, arXiv:2506.08733 (2025).
Additional references
10 papers in this index state this conjecture (2018–2025). The statement above is taken from the most recent of them; the others are arXiv:2504.10927, arXiv:2401.04697, arXiv:2008.09889, arXiv:2004.14732, arXiv:2003.09130, arXiv:1911.04727, arXiv:1910.05932, arXiv:1901.05920, arXiv:1805.03814.
Progress summary
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