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Preprint Number 759
759. Manuel Bodirsky and Peter Jonsson and Trung Van Pham The Reducts of the Homogeneous Binary Branching C-relation E-mail: Submission date: 11 August 2014 Abstract: 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. Mathematics Subject Classification: Keywords and phrases: |
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