A. Peter, C. G. Cholak, T. A. Jockusch, and . Slaman, On the strength of Ramsey's theorem for pairs, Journal of Symbolic Logic, vol.66, issue.01, pp.1-55, 2001.

J. Chubb, J. L. Hirst, and T. H. Mcnicholl, Reverse mathematics, computability, and partitions of trees, The Journal of Symbolic Logic, vol.74, issue.01, pp.201-215, 2009.
DOI : 10.2178/jsl/1231082309

J. Corduan, J. Marcia, J. Groszek, and . Mileti, Reverse mathematics and Ramsey's property for trees, The Journal of Symbolic Logic, vol.75, issue.03, pp.945-954, 2010.
DOI : 10.2178/jsl/1278682209

D. Damir and . Dzhafarov, Strong reductions between combinatorial principles

J. L. Damir-d-dzhafarov, T. J. Hirst, and . Lakins, Ramsey's theorem for trees: the polarized tree theorem and notions of stability, Archive for Mathematical Logic, vol.49, issue.3, pp.399-415, 2010.

P. Erdos and R. Rado, Combinatorial theorems on classifications of subsets of a given set, Proceedings of the London mathematical Society, vol.3, issue.1, pp.417-439, 1952.

E. Frittaion and A. Marcone, Linear extensions of partial orders and reverse mathematics, MLQ Math. Log. Q, vol.58, issue.6, 2012.
DOI : 10.1002/malq.201200025
URL : http://arxiv.org/pdf/1203.5207.pdf

. Denis-r-hirschfeldt, Slicing the truth, Institute for Mathematical Sciences, vol.28, 2014.

J. L. Hirst, Combinatorics in subsystems of second order arithmetic, 1987.

. Carl-g-jockusch, Ramsey's theorem and recursion theory, Journal of Symbolic Logic, vol.37, issue.2, pp.268-280, 1972.

G. Carl, R. Jockusch, and . Soare, ? 0 1 classes and degrees of theories, Transactions of the American Mathematical Society, vol.173, pp.33-56, 1972.

M. Lerman, R. Solomon, and H. Towsner, Separating principles below Ramsey's theorem for pairs, Journal of Mathematical Logic, vol.13, issue.02, p.1350007, 2013.

A. Montalbán, Open questions in reverse mathematics, Bulletin of Symbolic Logic, vol.17, issue.03, pp.431-454, 2011.

L. Patey, Iterative forcing and hyperimmunity in reverse mathematics, Evolving Computability, vol.9136, pp.291-301, 2015.
DOI : 10.3233/com-160062
URL : https://hal.archives-ouvertes.fr/hal-01888601

L. Patey, The strength of the tree theorem for pairs in reverse mathematics, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01888614

L. Patey, The weakness of being cohesive, thin or free in reverse mathematics, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01888606

J. G. Rosenstein, Linear orderings, Pure and Applied Mathematics, vol.98, 1982.

D. Scott, Algebras of sets binumerable in complete extensions of arithmetic, Proc. Sympos. Pure Math, vol.5, pp.117-121, 1962.

D. Seetapun and T. A. Slaman, On the strength of Ramsey's theorem, Notre Dame Journal of Formal Logic, vol.36, issue.4, pp.570-582, 1995.

. Joseph-r-shoenfield, On degrees of unsolvability, Annals of Mathematics, vol.69, issue.03, pp.644-653, 1959.

G. Stephen and . Simpson, Subsystems of Second Order Arithmetic, Japan E-mail address: frittaion@math.tohoku.ac.jp URL, 2009.