On sets with rank one in simple homogeneous structures
2015 (English)In: Fundamenta Mathematicae, ISSN 0016-2736, E-ISSN 1730-6329, Vol. 228, 223-250 p.Article in journal (Refereed) Published
We study definable sets D of SU-rank 1 in Meq, where M is a countable homogeneous and simple structure in a language with finite relational vocabulary. Each such D can be seen as a 'canonically embedded structure', which inherits all relations on D which are definable in Meq, and has no other definable relations. Our results imply that if no relation symbol of the language of M has arity higher than 2, then there is a close relationship between triviality of dependence and D being a reduct of a binary random structure. Somewhat more precisely: (a) if for every n≥2, every n-type p(x1,...,xn) which is realized in D is determined by its sub-2-types q(xi,xj)⊆p, then the algebraic closure restricted to D is trivial; (b) if M has trivial dependence, then D is a reduct of a binary random structure.
Place, publisher, year, edition, pages
2015. Vol. 228, 223-250 p.
model theory, homogeneous structure, simple theory, pregeometry, rank, reduct, random structure
Algebra and Logic
Research subject Mathematics
IdentifiersURN: urn:nbn:se:uu:diva-243006DOI: 10.4064/fm228-3-2ISI: 000352858400002OAI: oai:DiVA.org:uu-243006DiVA: diva2:785724