abstract:
On the one hand, finite graphs serve as one of the prime examples in logic and model theory; on the other hand, they also lead to a rich spectrum of results in analysis and "continuous mathematics".
We present a possible synthesis of these two lines in the particular area of graph limits and provide a unified treatment of various graph limit concepts by means of a combination of model theory and functional analysis.
We show how our setting extends the now classical notions of limits of dense graphs and of limits of bounded degree graphs.