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Let (L; C) be the (up to isomorphism unique) countable homogeneous structure carrying a binary branching C-relation. We study the reducts of (L; C), i.e., the structures with domain L that are first-order definable in (L; C). We show that up to existential interdefinability, there are finitely many such reducts. This implies that there are finitely many reducts up to first-order interdefinability, thus confirming a conjecture of Simon Thomas for the special case of (L; C). We also study the endomorphism monoids of such reducts and show that they fall into four categories.<p>Funding Agencies|European Research Council under the European Communitys Seventh Framework Programme (FP7) [257039]; Austrian Science Fund (FWF) [P27600]; Vietnam National Foundation for Science and Technology Development (NAFOSTED); Swedish Research Council (VR) [621-2012-3239]</p

THE REDUCTS OF THE HOMOGENEOUS BINARY BRANCHING C-RELATION