2 results
CORES OVER RAMSEY STRUCTURES
- Part of
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- Journal:
- The Journal of Symbolic Logic / Volume 86 / Issue 1 / March 2021
- Published online by Cambridge University Press:
- 01 February 2021, pp. 352-361
- Print publication:
- March 2021
-
- Article
- Export citation
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We prove that if an
$\omega $
-categorical structure has an
$\omega $
-categorical homogeneous Ramsey expansion, then so does its model-complete core.
THE REDUCTS OF THE HOMOGENEOUS BINARY BRANCHING C-RELATION
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- 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
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- Article
- Export citation
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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.
