Shelah–Hasson conjecture for strongly NIP ordered fields
Shelah–Hasson conjecture for strongly NIP ordered fields
Let be a strongly NIP ordered field. Such a field is almost real closed if it admits a henselian valuation whose residue field is real closed. Shelah–Hasson conjecture for ordered fields. Every strongly NIP ordered field is almost real closed. Equivalently, every strongly NIP ordered field that is not real closed admits a non-trivial -definable henselian valuation, where is the language of ordered rings. This is known for dp-minimal ordered fields, but remains open for general strongly NIP ordered fields.
Sources & referencesView supporting material
Primary source
Lothar Sebastian Krapp, Salma Kuhlmann and Gabriel Lehéricy, “Ordered fields dense in their real closure and definable convex valuations”, arXiv:2010.11832 (2020).
Additional references
3 papers in this index state this conjecture (2018–2020). The statement above is taken from the most recent of them; the others are arXiv:2010.14770, arXiv:1810.10377.
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