Date of Original Version

12-27-2014

Type

Working Paper

Abstract or Description

Our work builds on known results for k-uniform hypergraphs including the existence of limits, a Regularity Lemma and a Removal Lemma. Our main tool here is a theory of measures on ultraproduct spaces which establishes a correspondence between ultraproduct spaces and Euclidean spaces. First we show the existence of a limit object for convergent sequences of relational structures and as a special case, we retrieve the known limits for graphs and digraphs. Then we extend this notion to finite models of a fixed universal theory. We also state and prove a Regularity Lemma and a Removal Lemma. We will discuss connections between our work and Razborov's flag algebras as well.

Included in

Mathematics Commons

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Published In

Journal of Symbolic Logic, forthcoming.