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Relational structures determined by their finite induced substructures

  • I. M. Hodkinson (a1) and H. D. Macpherson (a2)


A countably infinite relational structure M is called absolutely ubiquitous if the following holds: whenever N is a countably infinite structure, and M and N have the same isomorphism types of finite induced substructures, there is an isomorphism from M to N. Here a characterisation is given of absolutely ubiquitous structures over languages with finitely many relation symbols. A corresponding result is proved for uncountable structures.


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Mathematical Institute, 24–29 St. Giles, Oxford OX1 3LB, England


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