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Relational Structures Determined by Their Finite Induced Substructures

I. M. Hodkinson and H. D. Macpherson
The Journal of Symbolic Logic
Vol. 53, No. 1 (Mar., 1988), pp. 222-230
DOI: 10.2307/2274440
Stable URL: http://www.jstor.org/stable/2274440
Page Count: 9
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Relational Structures Determined by Their Finite Induced Substructures
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Abstract

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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