Idiosynchromatic poetry (Q2341927): Difference between revisions

The author provides bounds for ordinal Ramsey numbers. This is done in two steps: for example, for (infinite) cardinals \(\kappa\) that satisfy \(\kappa\to(\kappa)^2_2\) the relation \(\kappa^2l\to(\kappa^2m,n)\) holds iff every three-coloured directed graph on \(l\) vertices contains an independent set of size \(m\) or a subtournament on \(n\) vertices in which all triples belong to a class of fifteen special configurations (called agreeable by the author); the next step is then to bound \(l\) in terms of \(m\) and \(n\) using this finite characterization. The result is a series of bounds on Ramsey numbers of the form \(r(\omega^2m,3)\) and \(r(\kappa\lambda,m,3)\).