A Miniaturisation of Ramsey's Theorem

摘要

We approximate the strength of the infinite Ramsey Theorem by iterating a finitary version. This density principle, in the style of Paris, together with PA will give rise to a first-order theory which achieves a lot of the strength of ACAo and the original infinitary version. To prove our result, we use a generalisation of the results by Bigorajska and Kotlarski about partitioning a-large sets.