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THE REDUCTS OF THE HOMOGENEOUS BINARY BRANCHING C-RELATION

Published online by Cambridge University Press:  01 December 2016

MANUEL BODIRSKY ,
PETER JONSSON  and
TRUNG VAN PHAM
MANUEL BODIRSKY
Affiliation:
INSTITUT FÜR ALGEBRA TU DRESDEN 01062 DRESDEN, GERMANY E-mail: manuel.bodirsky@tu-dresden.de
PETER JONSSON
Affiliation:
DEPARTMENT OF COMPUTER AND SYSTEM SCIENCE LINKÖPINGS UNIVERSITET SE-581 83 LINKÖPING, SWEDEN E-mail: peter.jonsson@liu.se
TRUNG VAN PHAM
Affiliation:
INSTITUT FÜR COMPUTERSPRACHEN THEORY AND LOGIC GROUP TECHNISCHE UNIVERSITÄT WIEN FAVORITENSTRASSE 9/E1852 A-1040 WIEN, AUSTRIA E-mail: pvtrung@logic.at
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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.

Keywords

03C0703C9820B2708A3505C5503C05omega-categoricityfirst-order reductstree-like structuresC-relationhomogeneous structuresmodel-completenessendomorphism monoids

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Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 4 , December 2016 , pp. 1255 - 1297
Copyright
Copyright © The Association for Symbolic Logic 2016 

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