On sets with rank one in simple homogeneous structures

• Autorzy: Ove Ahlman , Vera Koponen
• Języki publikacji: EN

Abstrakty

EN

We study definable sets D of SU-rank 1 in $ℳ^{eq}$, 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 $ℳ^{eq}$, 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 $q(x_{i},x_{j}) ⊆ p$, 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.

Kategorie tematyczne

• 03C15: Denumerable structures
• 03C45: Classification theory, stability and related concepts
• 03C50: Models with special properties (saturated, rigid, etc.)
• 03C30: Other model constructions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2015
• Tom: 228
• Numer: 3
• Strony: 223-250

Daty

wydano

2015

Twórcy

autor

Ove Ahlman

• Department of Mathematics, Uppsala University, Box 480, 75106 Uppsala, Sweden

autor

Vera Koponen

• Department of Mathematics, Uppsala University, Box 480, 75106 Uppsala, Sweden

Identyfikatory

DOI

10.4064/fm228-3-2