The strength of infinitary Ramseyan principles can be accessed by their densities

We conduct a model-theoretic investigation of three infinitary ramseyan statements: Ramsey Theorem for pairs and two colours (RT2), Canonical Ramsey Theorem for pairs (CRT) and Regressive Ramsey Theorem for pairs (RegRT). We prove theorems that approximate the logical strength of these principles by the strength of their finite iterations known as density principles. We then investigate their logical strength using strong initial segments of models of Peano Arithmetic, in the spirit of Paris-Kirby results. The article is concluded by a discussion of two further outreaches of densities. One concerns further investigations of the strength of Ramsey Theorem for pairs. The other one is about the asymptotic of the standard Ramsey function R2 2.