A cardinal characteristic can often be described as the smallest size of a family of sequences which has a given property. Instead of this traditional concern for a smallest realization of the given property, a basically new approach, taken in  and , asks for a realization whose members are sequences of labels that correspond to 1-way infinite paths in a labelled graph. We study this approach as such, establishing tools that are applicable to all these cardinal characteristics. As an application, we demonstrate the power of the tools developed by presenting a short proof of the bounded graph conjecture .
Nick Haverkamp. "Cardinal characteristics on graphs." J. Symbolic Logic 76 (1) 1 - 33, March 2011. https://doi.org/10.2178/jsl/1294170987