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Homogeneous 1‐based structures and interpretability in random structures
Author(s) -
Koponen Vera
Publication year - 2017
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201400096
Subject(s) - arity , mathematics , countable set , homogeneous , combinatorics , simple (philosophy) , discrete mathematics , rank (graph theory) , equivalence (formal languages) , equivalence relation , philosophy , epistemology
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.