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THE REDUCTS OF THE HOMOGENEOUS BINARY BRANCHING C-RELATION
Published online by Cambridge University Press: 01 December 2016
Abstract
Let ($\rm L$;C) be the (up to isomorphism unique) countable homogeneous structure carrying a binary branching C-relation. We study the reducts of (
$\rm L$;C), i.e., the structures with domain
$\rm L$ that are first-order definable in (
$\rm L$;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 (
$\rm L$;C). We also study the endomorphism monoids of such reducts and show that they fall into four categories.
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- Copyright © The Association for Symbolic Logic 2016
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