Submission date: 18 January 2016.

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 NTP_2. We use this to deduce the first general results about definable sets in NTP_2 expansions of ( R, < , + ).

Mathematics Subject Classification: Primary 03C45, Secondary 03C64, 03D05, 28A80, 54F45

Keywords and phrases:

Full text arXiv 1601.04555: pdf, ps.