A conjectural classification of strongly dependent fields

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Bulletin of Symbolic Logic 25 (2):182-195 (2019)
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Abstract

We survey the history of Shelah’s conjecture on strongly dependent fields, give an equivalent formulation in terms of a classification of strongly dependent fields and prove that the conjecture implies that every strongly dependent field has finite dp-rank.

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10.1017/bsl.2019.13

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Citations of this work

Definable V-topologies, Henselianity and NIP.Yatir Halevi, Assaf Hasson & Franziska Jahnke - 2019 - Journal of Mathematical Logic 20 (2):2050008.
Dp-finite fields I(B): Positive characteristic.Will Johnson - 2021 - Annals of Pure and Applied Logic 172 (6):102949.
Dp-finite fields I(A): The infinitesimals.Will Johnson - 2021 - Annals of Pure and Applied Logic 172 (6):102947.

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References found in this work

Theories without the tree property of the second kind.Artem Chernikov - 2014 - Annals of Pure and Applied Logic 165 (2):695-723.
Dp-minimal valued fields.Franziska Jahnke, Pierre Simon & Erik Walsberg - 2017 - Journal of Symbolic Logic 82 (1):151-165.
The canonical topology on dp-minimal fields.Will Johnson - 2018 - Journal of Mathematical Logic 18 (2):1850007.
Cell decompositions of C-minimal structures.Deirdre Haskell & Dugald Macpherson - 1994 - Annals of Pure and Applied Logic 66 (2):113-162.
On dp-minimality, strong dependence and weight.Alf Onshuus & Alexander Usvyatsov - 2011 - Journal of Symbolic Logic 76 (3):737 - 758.

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