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1 results

  • THE REDUCTS OF THE HOMOGENEOUS BINARY BRANCHING C-RELATION

  • MANUEL BODIRSKY, PETER JONSSON, TRUNG VAN PHAM
  • Journal:
    The Journal of Symbolic Logic / Volume 81 / Issue 4 / December 2016
    Published online by Cambridge University Press:
    01 December 2016, pp. 1255-1297
    Print publication:
    December 2016

  • 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.