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Preprint Number 867
867. Gabriel Conant
An axiomatic approach to free amalgamation
Submission date: 4 May 2015.
We use axioms of abstract ternary relations to define the notion of a free amalgamation theory. This notion encompasses many prominent examples of countable structures in relational languages, which have free amalgamation with respect to algebraically closed substructures. Such examples include the random graph, the generic K_n-free graph and (K_n+K_3)-free graph, and certain Hrushovski constructions defined from a predimension and "good" control function. We unify and generalize previous work of Evans & Wong and Patel to prove that any free amalgamation theory is NSOP_4. We then show that any free amalgamation theory has weak elimination of imaginaries, which yields new examples of rosy theories.
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