@article{d962c2ad27684ff3ab6877370938a9a3,
title = "A CONJECTURAL CLASSIFICATION OF STRONGLY DEPENDENT FIELDS",
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.",
keywords = "NIP, Shelah's conjecture, strong dependence, valued fields",
author = "Yatir Halevi and Assaf Hasson and Franziska Jahnke",
note = "Funding Information: We would like to thank S. Anscombe for allowing us to include the discussion concluding this note, for her comments and suggestions. Supported by ISF grant No. 181/16. Funded by the Deutsche Forschungsgemeinschaft (DFG, GermanResearch Foundation) under Germany's Excellence Strategy EXC 2044-390685587, Mathematics M{\"u}nster: Dynamics-Geometry-Structure and the CRC 878. Partially supported by the European Research Council grant 338821, by ISF grant No. 181/16 and ISF grant No. 1382/15. Publisher Copyright: Copyright {\textcopyright} 2019 The Association for Symbolic Logic.",
year = "2019",
month = jun,
day = "1",
doi = "10.1017/bsl.2019.13",
language = "English",
volume = "25",
pages = "182--195",
journal = "Bulletin of Symbolic Logic",
issn = "1079-8986",
publisher = "Cambridge University Press",
number = "2",
}