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Fundamenta Mathematicae

2015 | 228 | 3 | 223-250
Tytuł artykułu

On sets with rank one in simple homogeneous structures

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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.
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Tom
Numer
Strony
223-250
Opis fizyczny
Daty
wydano
2015
Twórcy
autor
• Department of Mathematics, Uppsala University, Box 480, 75106 Uppsala, Sweden
autor
• Department of Mathematics, Uppsala University, Box 480, 75106 Uppsala, Sweden
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