Abstract
A partial order is called semilinear if the upper bounds of each element are linearly ordered and any two elements have a common upper bound. There exists, up to isomorphism, a unique countable existentially closed semilinear order, which we denote by (S-2; <=).
We study the reducts of (S-2; <=), i. e. the relational structures with domain S-2, all of whose relations are first-order definable in (S-2; <=). Our main result is a classification of the model-complete cores of the reducts of S-2.
From this, we also obtain a classification of reducts up to first-order interdefinability, which is equivalent to a classification of all subgroups of the full symmetric group on S-2 that contain the automorphism group of (S-2; <=) and are closed with respect to the pointwise convergence topology.