-conservation of combinatorial principles weaker than Ramsey鈥檚 theorem for pairs

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• 作者：C.T. Chong^a ; ^{chongct@gmail.com} ; ^{chongct@math.nus.edu.sg} ; Theodore A. Slaman^b ; ^{slaman@math.berkeley.edu} ; Yue Yang^a ; ^{matyangy@nus.edu.sg}
• 关键词：Reverse mathematics ; -conservation ; ; -bounding ; Combinatorial principles ; Ascending/descending sequence ; Chain/antichain ; Cohesiveness
• 刊名：Advances in Mathematics
• 出版年：2012
• 期刊代码：62_00018708
• 类别：mt
• 出版时间：20 June, 2012
• 卷：230
• 期：3
• 页码：1060-1077
• 文件大小：255 K

摘要

We study combinatorial principles weaker than Ramsey鈥檚 theorem for pairs over the (recursive comprehension axiom) system with -bounding. It is shown that the cohesiveness (), ascending and descending sequence (), and chain/antichain () principles are all -conservative over -bounding. In particular, none of these principles proves -induction.