2014/12/27 by Ashwini Aroskar, James Cummings, Aroskar, Ashwini +1 · 1 citation
Mathematics · #03C20 #05C99 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.1412.8084
openalex publication_date 2014/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.