Title: On the role of the Collection Principle for Sigma-0-2-formulas in second-order reverse mathematics.

Abstract:
This is joint work with Chitat Chong and Yue Yang.

We show that the principle PART from Hirschfeldt and Shore [2007] is
equivalent to the Sigma^0_2-Bounding principle BSigma^0_2 over RCA_0,
answering one of their open questions.

Our work also fills a gap in a proof in Cholak, Jockusch and Slaman [2001] by
showing that D^2_2 implies BSigma^0_2 and is thus indeed equivalent to Stable
Ramsey’s Theorem for Pairs SRT^2_2.

This also allows us to conclude that the combinatorial principles IPT, SPT and
SIPT defined by Dzhafarov and Hirst [2009] all imply BSigma^0_2, and thus that
SPT and SIPT are both equivalent to SRT^2_2 as well.

Our proof uses the notion of a bi-tame cut in models of arithmetic, the
existence of which we show to be equivalent, over RCA_0, to the failure of
BSigma^0_2.