Afshari, B. and Rathjen, M. [2009], Reverse mathematics and well-ordering principles: A pilot study, Annals of Pure and Applied Logic, vol. 160, pp. 231–237.

Aharoni, R., Magidor, M., and Shore, R. A. [1992], On the strength of Köonig's duality theorem for infinite bipartite graphs, Journal of Combinatorial Theory (B), vol. 54, pp. 257–290.

Blum, L., Cucker, F., Shub, M., and Smale, S. [1998], Complexity and real computation, Springer-Verlag, New York.

Cholak, P. A., Jockusch, C. G. Jr., and Slaman, T. A. [2001], On the strength of Ramsey's theorem for pairs, The Journal of Symbolic Logic, vol. 66, pp. 1–55.

Chong, C. T. [1984], Techniques of admissible recursion theory, Lecture Notes in Mathematics, vol. 1106, Springer-Verlag, Berlin.

Chong, C. T., Lempp, S., and Yang, Y. [2010], On the role of the collection principle for -formulas in second-order reverse mathematics, Proceedings of the American Mathematical Society, vol. 13, pp. 1093–1100.
Downey, R., Hirschfeldt, D. R., Lempp, S., and Solomon, R. [2001], A set with no infinite low subset in either it or its complement, The Journal of Symbolic Logic, vol. 66, pp. 1371–1381.
Dzhafarov, D. and Hirst, J. [2009], The polarized Ramsey theorem, Archive for Mathematical Logic, vol. 48, pp. 141–157.

Fenstad, Jens Erik [1980], General recursion theory: An axiomatic approach, Perspectives in Mathematical Logic, Springer-Verlag, Berlin–New York.

Friedman, H. [1967], Subsystems of set theory and analysis, Ph.D. thesis, M.I.T..

Friedman, H. [1971], Higher set theory and mathematical practice, Annals of Mathematical Logic, vol. 2, pp. 325–357.

Friedman, H. [1975], Some systems of second order arithmetic and their use, Proceedings of the International Congress of Mathematicians, Vancouver 1974, vol. 1, pp. 235–242.

Friedman, H., Robertson, N., and Seymour, P. [1987], The metamathematics of the graph minor theorem, Logic and combinatorics (Simpson, S., editor), Contemporary Mathematics, American Mathematical Society, Providence.

Hajek, P. and Pudlak, P. [1998], Metamathematics of first order arithmetic, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 2nd printing.

Hirschfeldt, D. R., Lange, K., and Shore, R. A. [2012], *The homogeneous model theorem*, in preparation.

Hirschfeldt, D. R. and Shore, R. A. [2007], Combinatorial principles weaker than Ramsey's theorem for pairs, The Journal of Symbolic Logic, vol. 72, pp. 171–206.

Hirschfeldt, D. R., Shore, R. A., and Slaman, T. A. [2009], The atomic model theorem, Transactions of the American Mathematical Society, vol. 361, pp. 5805–5837.

Jockusch, C. G. Jr. and Soare, R. I. [1972],
classes and degrees of theories, Transactions of the American Mathematical Society, vol. 173, pp. 33–56.
Jullien, P. [1960], **
***Contribution à l'étude des types d'ordre dispersés*
, Ph.D. thesis, Marseille.

Keisler, H. J. [2006], *Nonstandard arithmetic and reverse mathematics*, this Bulletin, vol. 12, pp. 100–125.

Keisler, H. J. [2011], Nonstandard arithmetic and recursive comprehension, Annals of Pure and Applied Logic, to appear.

Kirby, L. and Paris, J. [1978], Σ_{n} collection schemes in arithmetic, Logic colloquium '77 (Macintyre, A., Pacholski, L., and Paris, J., editors), Studies in Logic and the Foundations of Mathematics, North-Holland, Amsterdam, pp. 199–209.

Kohlenbach, U. [2005], Higher order reverse mathematics, Reverse mathematics 2001 (Simpson, S., editor), Lecture Notes in Logic, vol. 21, Association for Symbolic Logic and A. K. Peters, Wellesley, MA, pp. 281–295.

Kohlenbach, U. [2008], Applied proof theory: Proof interpretations and their use in mathematics, Springer Monographs in Mathematics, Springer, Berlin.

Lerman, M. [1972], On suborderings of the α-recursively enumerable α-degrees, Annals of Mathematical Logic, vol. 4, pp. 369–392.

Lovasz, L. and Plummer, M. D. [1986], Matching theory, Annals of Discrete Mathematics, vol. 29, North-Holland, Amsterdam.

Marcone, A. and Montalbán, A. [2009], On Fraïssé's conjecture for linear orders of finite Hausdorff rank, Annals of Pure and Applied Logic, vol. 160, pp. 355–367.

Marcone, A. and Montalbán, A. [2011], *The Veblen functions for computability theorists*, to appear.

Martin, D. A. [1974], *Analysis ⊢ -determinacy*, circulated handwritten notes dated 04 24, 1974.
Martin, D. A. [1974a], *
-determinacy*, circulated handwritten notes dated 03 20, 1974.
Martin, D. A. [1975], Borel determinacy, Annals of Mathematics, vol. 102, pp. 363–371.

Martin, D. A. [n.d.], *Determinacy*, circulated drafts, about 578 pp.

MedSalem, M. O. and Tanaka, K. [2007],
-determinacy, comprehension and induction, The Journal of Symbolic Logic, vol. 72, pp. 452–462.
MedSalem, M. O. and Tanaka, K. [2008], Weak determinacy and iterations of inductive definitions, Computational prospects of infinity, part II: Presented talks (Chong, C., Feng, Q., Slaman, T. A., Woodin, W. H., and Yang, Y., editors), Lecture Note Series, World Scientific, Singapore, pp. 333–353.

Moldestad, J. [1977], Computations in higher types, Lecture Notes in Mathematics, vol. 574, Springer-Verlag, Berlin.

Montalbán, A. [2006], Indecomposable linear orderings and hyperarithmetic analysis, The Journal of Mathematical Logic, vol. 6, pp. 89–120.

Montalbán, A. and Shore, R. A. [2011], *The limits of determinacy in second order arithmetic*, to appear.

Mummert, C. and Simpson, S. G. [2005], *Reverse mathematics and comprehension*, this Bulletin, vol. 11, pp. 526–533.
Neeman, I. [2011], *The strength of Jullien's indecomposability theorem*, to appear.

Neeman, I. [2012], *Necessary uses of induction in a reversal*, to appear.
Nemoto, T., MedSalem, M. O., and Tanaka, K. [2007], Infinite games in the Cantor space and subsystems of second order arithmetic, MLQ. Mathematical Logic Quarterly, vol. 53, pp. 226–236.

Odifreddi, P. [1989], Classical recursion theory I, North-Holland, Elsevier, Amsterdam.

Odifreddi, P. [1999], Classical recursion theory II, North-Holland, Elsevier, Amsterdam.

Rathjen, M. and Weiermann, A. [2011], Reverse mathematics and well-ordering principles, to appear.

Rogers, H. Jr. [1967], Theory of recursive functions and effective computability, McGraw-Hill, New York.

Rosenstein, J. [1982], Linear orderings, Academic Press, New York–London.

Sacks, G. E. [1990], Higher recursion theory, Perspectives in Mathematical Logic, Springer-Verlag, Berlin.

Schwichtenberg, H. and Wainer, S. [2011], Proofs and computations, Perspectives in Logic, Association for Symbolic Logic and Cambridge University Press, New York, to appear.

Shore, R. A. [1972], Priority arguments in α-recursion theory, Ph.D. thesis, M.I.T..

Shore, R. A. [1993], On the strength of Fraïssé's conjecture, Logical methods (Crossley, J. N. C., Remmel, J., Shore, R. A., and Sweedler, M., editors), Birkhäuser, Boston, pp. 782–813.

Shore, R. A. [2007], Direct and local definitions of the Turing jump, Journal of Mathematical Logic, vol. 7, pp. 229–262.

Shore, R. A. [2011], *Reverse mathematics, countable and uncountable: a computational approach*, to appear.

Shore, R. A. and Slaman, T. A. [1999], Defining the Turing jump, Mathematical Research Letters, vol. 6, pp. 711–722.

Simpson, S. G. [1985], Nonprovability of certain combinatorial properties of finite trees, Harvey Friedman's research on the foundations of mathematics (Harrington, L. A., Morley, M. D., Scedrov, A., and Simpson, S. G., editors), Studies in Logic and the Foundations of Mathematics, vol. 117, North-Holland, Amsterdam, pp. 87–118.

Simpson, S. G. [1994], On the strength of Köonig's duality theorem for countable bipartite graphs, The Journal of Symbolic Logic, vol. 59, pp. 113–123.

Simpson, S. G. [2009], Subsystems of second order arithmetic, 2nd ed., Perspectives in Logic, Association for Symbolic Logic and Cambridge University Press, New York.

Slaman, T. A. [1991], Degree structures, Proceedings of the International Congress of Mathematicians, Kyoto 1990, Springer-Verlag, Tokyo, pp. 303–316.

Slaman, T. A. [2008], Global properties of the Turing degrees and the Turing jump, Computational prospects of infinity. Part I: Tutorials (Chong, C. T., Feng, Q, Slaman, T. A., Woodin, W. H., and Yang, Y., editors), Lecture Notes Series, vol. 14, World Scientific, pp. 83–101.

Soare, R. I. [1987], Recursively enumerable sets and degrees, Springer-Verlag, Berlin.

Steel, J. [1976], Determinateness and subsystems of analysis, Ph.D. thesis, University of California, Berkeley.

Steel, J. [1978], Forcing with tagged trees, Annals of Mathematical Logic, vol. 15, pp. 55–74.

Tanaka, K. [1990], Weak axioms of determinacy and subsystems of analysis I: games, Zeitschrift für mathematische Logik und Grundlagen der Mathmatik, vol. 36, pp. 481–491.
Tanaka, K. [1991], Weak axioms of determinacy and subsystems of analysis II ( games), Annals of Pure and Applied Logic, vol. 52, pp. 181–193.
Welch, P. [2009], *Weak systems of determinacy and arithmetical quasi-inductive definitions*, preprint.

Yokoyama, K. [2007], Non-standard analysis in ACA_{0} and Riemann mapping theorem, MLQ. Mathematical Logic Quarterly, vol. 53, pp. 132–146.

Yokoyama, K. [2009], Standard and non-standard analysis in second order arithmetic, D.S. thesis, Tohoku University, available as **
***Tohoku Mathematical Publications*
vol. 34 (2009).