On VC-minimal fields and dp-smallness

Archive for Mathematical Logic 53 (5-6):503-517 (2014)
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Abstract

In this paper, we show that VC-minimal ordered fields are real closed. We introduce a notion, strictly between convexly orderable and dp-minimal, that we call dp-small, and show that this is enough to characterize many algebraic theories. For example, dp-small ordered groups are abelian divisible and dp-small ordered fields are real closed.

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10.1007/s00153-014-0376-9

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Citations of this work

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.
Definable V-topologies, Henselianity and NIP.Yatir Halevi, Assaf Hasson & Franziska Jahnke - 2019 - Journal of Mathematical Logic 20 (2):2050008.

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References found in this work

On dp-minimal ordered structures.Pierre Simon - 2011 - Journal of Symbolic Logic 76 (2):448 - 460.
Dp-Minimality: Basic Facts and Examples.Alfred Dolich, John Goodrick & David Lippel - 2011 - Notre Dame Journal of Formal Logic 52 (3):267-288.
On dp-minimality, strong dependence and weight.Alf Onshuus & Alexander Usvyatsov - 2011 - Journal of Symbolic Logic 76 (3):737 - 758.
Notes on the stability of separably closed fields.Carol Wood - 1979 - Journal of Symbolic Logic 44 (3):412-416.

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