Puritz-style characterization of Ramsey pairs

Characterize Ramsey pairs in terms of standard functions by establishing an analogue of Puritz’ characterization of tensor pairs.

Background

A tensor pair admits a simple characterization through the relative behavior of standard functions applied to its coordinates, known as Puritz’ Theorem. The paper develops several necessary properties of Ramsey pairs but does not obtain an analogous complete characterization. Such a result could facilitate the study of further infinitary Ramsey partition-regularity problems.