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THE REDUCTS OF THE HOMOGENEOUS BINARY BRANCHING C-RELATION
Technical University of Dresden, Germany.
Linköping University, Department of Computer and Information Science, Software and Systems. Linköping University, Faculty of Science & Engineering.
Vienna University of Technology, Austria.
2016 (English)In: Journal of Symbolic Logic (JSL), ISSN 0022-4812, E-ISSN 1943-5886, Vol. 81, no 4, p. 1255-1297Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
CAMBRIDGE UNIV PRESS , 2016. Vol. 81, no 4, p. 1255-1297
Keyword [en]
omega-categoricity; first-order reducts; tree-like structures; C-relation; homogeneous structures; model-completeness; endomorphism monoids
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:liu:diva-133891DOI: 10.1017/jsl.2016.37ISI: 000390118100003OAI: oai:DiVA.org:liu-133891DiVA, id: diva2:1065079
Note

Funding Agencies|European Research Council under the European Communitys Seventh Framework Programme (FP7) [257039]; Austrian Science Fund (FWF) [P27600]; Vietnam National Foundation for Science and Technology Development (NAFOSTED); Swedish Research Council (VR) [621-2012-3239]

Available from: 2017-01-13 Created: 2017-01-13 Last updated: 2017-11-29

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