Combinatorial principles between \mathrm{R}\mathrm{R}{\mathrm{T}}_{\mathrm{2}}^{\mathrm{2}} and \mathrm{R}{\mathrm{T}}_{\mathrm{2}}^{\mathrm{2}}

Abstract

We study the strength of some combinatorial principles weaker than Ramsey theorem for pairs over RCA₀. First, we prove that Rainbow Ramsey theorem for pairs does not imply Thin Set theorem for pairs. Furthermore, we get some other related results on reverse mathematics using the same method. For instance, Rainbow Ramsey theorem for pairs is strictly weaker than Erdös-Moser theorem under RCA₀.

Key words： Reverse mathematics; thin set; free set; Erdös-Moser theorem; Rainbow Ramsey theorem

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