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On Constraints And Dividing In Ternary Homogeneous Structures
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
2018 (English)In: Journal of Symbolic Logic (JSL), ISSN 0022-4812, E-ISSN 1943-5886, Vol. 83, no 4, p. 1691-1721Article in journal (Refereed) Published
Abstract [en]

Let M be ternary, homogeneous and simple. We prove that if M is finitely constrained, then it is supersimple with finite SU-rank and dependence is k-trivial for some k < omega and for finite sets of real elements. Now suppose that, in addition, M is supersimple with SU-rank 1. If M is finitely constrained then algebraic closure in M is trivial. We also find connections between the nature of the constraints of M, the nature of the amalgamations allowed by the age of M, and the nature of definable equivalence relations. A key method of proof is to "extract" constraints (of M) from instances of dividing and from definable equivalence relations. Finally, we give new examples, including an uncountable family, of ternary homogeneous supersimple structures of SU-rank 1.

Place, publisher, year, edition, pages
2018. Vol. 83, no 4, p. 1691-1721
Keywords [en]
model theory, homogeneous structure, simple theory, constraint, dividing, amalgamation
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:uu:diva-373241DOI: 10.1017/jsl.2018.61ISI: 000454236900023OAI: oai:DiVA.org:uu-373241DiVA, id: diva2:1278326
Available from: 2019-01-14 Created: 2019-01-14 Last updated: 2019-01-14Bibliographically approved

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Koponen, Vera

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