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\iteman{io-port 05688759}
\itemau{Chong, C.T.; Lempp, Steffen; Yang, Yue}
\itemti{On the role of the collection principle for $\Sigma ^0_2$-formulas in second-order reverse mathematics.}
\itemso{Proc. Am. Math. Soc. 138, No. 3, 1093-1100 (2010).}
\itemab
The authors introduce the notion of bi-tame cuts in models of arithmetic, showing that the bounding principle B$\Sigma^0_2$ fails in precisely those models containing a bi-tame cut. Using this new characterization of B$\Sigma^0_2$, they show that B$\Sigma^0_2$ is equivalent over RCA$_0$ to the principle PART of {\it D. R. Hirschfeldt} and {\it R. A. Shore} [``Combinatorial principles weaker than Ramsey's theorem for pairs'', J. Symb. Log. 72, No. 1, 171--206 (2007; Zbl 1118.03055)]. They also show that D$^2_2$ implies B$\Sigma^0_2$, completing the proof that D$^2_2$ is equivalent to the stable Ramsey Theorem SRT$^2_2$ over RCA$_0$ and closing a gap in the argument in [{\it P. A. Cholak, C. G. Jockusch} and {\it T. A. Slaman}, ``On the strength of Ramsey's theorem for pairs'', J. Symb. Log. 66, No. 1, 1--55 (2001; Zbl 0977.03033)]. (The gap was noted in a corrigendum [J. Symb. Log. 74, No. 4, 1438--1439 (2009; Zbl 1182.03107)].) Additional consequences of the fact that D$^2_2$ implies B$\Sigma^0_2$ include collapsing much of the hierarchy of polarized Ramsey theorems listed in [{\it D. D. Dzhafarov} and {\it J. L. Hirst}, ``The polarized Ramsey's theorem'', Arch. Math. Logic 48, No. 2, 141--157 (2009; Zbl 1172.03007)].
\itemrv{Jeffry L. Hirst (Boone)}
\itemcc{}
\itemut{reverse mathematics; $\Sigma^0_2$-bounding; linear order; tame cut; bi-tame cut; Ramsey's Theorem; polarized Ramsey's Theorem}
\itemli{doi:10.1090/S0002-9939-09-10115-6}
\end