On the Role of the Collection Principle for Σ 02-formulas in Second-order Reverse Mathematics

  title={On the Role of the Collection Principle for Σ 02-formulas in Second-order Reverse Mathematics},
  author={Chi Tat Chong and Steffen Lempp and Yue Yang},
We show that the principle PART from Hirschfeldt and Shore is equivalent to the Σ2-Bounding principle BΣ 0 2 over RCA0, answering one of their open questions. Furthermore, we also fill a gap in a proof of Cholak, Jockusch and Slaman by showing that D2 2 implies BΣ 0 2 and is thus indeed equivalent to Stable Ramsey’s Theorem for Pairs (SRT2). This also allows us to conclude that the combinatorial principles IPT2, SPT 2 2 and SIPT 2 2 defined by Dzhafarov and Hirst all imply BΣ2 and thus that SPT… CONTINUE READING

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