Yuri Gurevich z Motivated by computer science challenges, we suggest to extend the approach and methods of nite model theory beyond nite structures. We study de nability issues and their relation to complexity onmeta nite structures which typically consist of (i) a primary part, which is a nite structure, (ii) a secondary part, which is a (usually in nite) structure that can be viewed as a structured domain of numerical objects, and (iii) a set of \weight " functions from the rst part into the second. We discuss model-theoretic properties of meta nite structures, present results on descriptive complexity, andsketch some potential applications.
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