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Mathematics
Set Theory

Unifying Themes in Finite Model Theory

Profile image of Erich GrädelErich Grädel

2007, Texts in Theoretical Computer Science an EATCS Series

https://doi.org/10.1007/3-540-68804-8_1
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26 pages

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Abstract

One of the fundamental insights of mathematical logic is that our understanding of mathematical phenomena is enriched by elevating the languages we use to describe mathematical structures to objects of explicit study. If mathematics is the science of pattern, then the media through which we discern patterns, as well as the structures in which we discern them, command our attention. It is this aspect of logic which is most prominent in model theory, "the branch of mathematical logic which deals with the relation between a formal language and its interpretations" . No wonder, then, that mathematical logic, in general, and finite model theory, the specialization of model theory to finite structures, in particular, should find manifold applications in computer science: from specifying programs to querying databases, computer science is rife with phenomena whose understanding requires close attention to the interaction between language and structure.

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