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Preprint Number 697
697. Vera Koponen
Homogeneous 1-based structures and interpretability in random structures
Submission date: 15 March 2014.
Let V be a finite relational vocabulary in which no symbol has arity greater than 2. Let M be countable V-structure which is homogeneous, simple and 1-based. The first main result says that if M is, in addition, primitive, then it is strongly interpretable in a random structure. The second main result, which generalizes the first, implies (without the assumption on primitivity) that if M is coordinatized by a set with SU-rank 1 and there is no definable (without parameters) nontrivial equivalence relation on M with only finite classes, then M is strongly interpretable in a random structure.
Mathematics Subject Classification: 03C15, 03C50, 03C45, 03C10
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