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 ACA0 and the original infinitary version. To prove our result, we use a generalisation of the results by Bigorajska and Kotlarski about partitioning α-large sets. © 2010 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
De Smet, M., & Weiermann, A. (2010). A miniaturisation of Ramsey’s theorem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6158 LNCS, pp. 118–125). https://doi.org/10.1007/978-3-642-13962-8_13
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