Metric Dimensions and Tameness in Expansions of the Real Field

On the real quadratic fields with certain continued fraction expansions and fundamental units

The purpose of this paper is to investigate the real quadratic number fields $Q(sqrt{d})$ which contain the specific form of the continued fractions expansions of integral basis element  where $dequiv 2,3( mod  4)$ is a square free positive integer. Besides, the present paper deals with determining the fundamental unit$$epsilon _{d}=left(t_d+u_dsqrt{d}right) 2left.right > 1$$and  $n_d$ and $m_d...

Interpreting the Monadic Second Order Theory of One Successor in Expansions of the Real Line

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, <,+). The goal of th...

On the Topology of Metric Spaces Definable in o-minimal expansions of fields

We study the topology of metric spaces which are definable in o-minimal expansions of ordered fields. We show that a definable metric space either contains an infinite definable discrete set or is definably homeomorphic to a definable set equipped with its euclidean topology. This implies that a separable metric space which is definable in an o-minimal expansion of the real field is definably h...

Decidability and Tameness in the Theory of Finite Semigroups

POINTWISE PSEUDO-METRIC ON THE L-REAL LINE

In this paper, a pointwise pseudo-metric function on the L-realline is constructed. It is proved that the topology induced by this pointwisepseudo-metric is the usual topology.