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 g...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 ErdSs- Moser theorem under RCA0.展开更多
基金Acknowledgements The author thanks Prof. Wei Wang for his valuable insights and helpful comments. He also thanks Profs. Chitat Chong, Qi Feng, and Yue Yang for providing chances to participate in a series of logic programs held by MCM of CAS and IMS of NUS. This work was partially supported by the National Natural Science Foundation of China （Grant No. 11001281） and the Basic Research Foundation of Jilin University, China （No. 450060502080）.
文摘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 ErdSs- Moser theorem under RCA0.
