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Preprint Number 697

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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

Keywords and phrases:

Full text arXiv 1403.3757: pdf, ps).

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