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Interpreting the monadic second order theory of one successor in expansions of the real line

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Abstract

We give sufficient conditions for a first order expansion of the real line to define the standard model of the monadic second order theory of one successor. Such an expansion does not satisfy any of the combinatorial tameness properties defined by Shelah, such as NIP or even NTP2. We use this to deduce the first general results about definable sets in NTP2 expansions of (R,<, +).

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Authors and Affiliations

  1. Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, IL, 61801, USA

    Philipp Hieronymi & Erik Walsberg

Authors
  1. Philipp Hieronymi
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  2. Erik Walsberg
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Corresponding author

Correspondence to Philipp Hieronymi.

Additional information

The first author was partially supported by NSF grant DMS-1300402.

The second author was supported by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC Grant agreement no. 291111/ MODAG.

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Hieronymi, P., Walsberg, E. Interpreting the monadic second order theory of one successor in expansions of the real line. Isr. J. Math. 224, 39–55 (2018). https://doi.org/10.1007/s11856-018-1635-y

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  • DOI: https://doi.org/10.1007/s11856-018-1635-y

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