Limits, Regularity and Removal for Finite Structures
Logic
2014-12-30 v1 Combinatorics
Abstract
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.
Cite
@article{arxiv.1412.8084,
title = {Limits, Regularity and Removal for Finite Structures},
author = {Ashwini Aroskar and James Cummings},
journal= {arXiv preprint arXiv:1412.8084},
year = {2014}
}