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On VC-minimal fields and dp-smallness

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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Correspondence to Vincent Guingona.

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The author was supported by NSF Grant DMS-0838506.

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Guingona, V. On VC-minimal fields and dp-smallness. Arch. Math. Logic 53, 503–517 (2014). https://doi.org/10.1007/s00153-014-0376-9

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  • DOI: https://doi.org/10.1007/s00153-014-0376-9

Keywords

  • Convexly orderable
  • VC-minimal
  • Ordered fields

Mathematics Subject Classification (2010)

  • 03C60
  • 03C45
  • 12J15