Definability with a predicate for a semi-linear set

We settle a number of questions concerning definability in first order logic with an extra predicate symbol ranging over semi-linear sets. We give ne v results both on the positive and negative side: we show that in first-order logic one cannot query a semi-linear set as to whether or not it contains a line. or whether or not it contains, the line segment between two given points, However. we show that some of these queries become definable if one makes small restrictions on the semi-linear sets considered.