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Binary primitive homogeneous simple structures
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2017 (English)In: Journal of Symbolic Logic (JSL), ISSN 0022-4812, E-ISSN 1943-5886, Vol. 82, no 1, p. 183-207Article in journal (Refereed) Published
Abstract [en]

Suppose that M is countable, binary, primitive, homogeneous, and simple. We prove that the SU-rank of the complete theory of M is 1 and hence 1-based. It follows that M is a random structure. The conclusion that M is a random structure does not hold if the binarity condition is removed, as witnessed by the generic tetrahedron-free 3-hypergraph. However, to show that the generic tetrahedron-free 3-hypergraph is 1-based requires some work (it is known that it has the other properties) since this notion is defined in terms of imaginary elements. This is partly why we also characterize equivalence relations which are definable without parameters in the context of omega-categorical structures with degenerate algebraic closure. Another reason is that such characterizations may be useful in future research about simple (nonbinary) homogeneous structures.

Place, publisher, year, edition, pages
2017. Vol. 82, no 1, p. 183-207
Keywords [en]
model theory, homogeneous structure, simple theory, random structure
National Category
Algebra and Logic
Research subject
Mathematical Logic
Identifiers
URN: urn:nbn:se:uu:diva-320741DOI: 10.1017/jsl.2016.51ISI: 000397110700011OAI: oai:DiVA.org:uu-320741DiVA, id: diva2:1090599
Available from: 2017-04-24 Created: 2017-04-24 Last updated: 2017-04-26Bibliographically approved

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Koponen, Vera

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