The Reducts of the Homogeneous Binary Branching C-relation

Manuel Bodirsky; Peter Jonsson; Trung Van Pham

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arXiv · 1408.2554

The Reducts of the Homogeneous Binary Branching C-relation

Manuel Bodirsky·Peter Jonsson·Trung Van Pham

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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.

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BibTeX RIS

Manuel Bodirsky, Peter Jonsson, Trung Van Pham. 2014-08-11. The Reducts of the Homogeneous Binary Branching C-relation. https://arxiv.org/abs/1408.2554

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