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Preprint Number 770
770. Manuel Bodirsky, David Bradley-Williams, Michael Pinsker, András Pongrácz
The universal homogeneous binary tree
Submission date: 7 September 2014.
A partial order is called semilinear iff 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 semilinear order which is dense, unbounded, binary branching, and without joins. We study the reducts of this semilinear order, that is, the relational structures which are first-order definable in it. Our main result is a classification of the model-complete cores of those reducts. From this, we also obtain a classification of reducts up to first-order interdefinability, which is equivalent to a classification of all closed permutation groups that contain the automorphism group of the semilinear order.
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