Brattka, V. and Gherardi, G., Weihrauch degrees, omniscience principles and weak computability, this Journal, vol. 76 (2011), no. 1, pp. 143–176.
Brattka, V., Gherardi, G., and Marcone, A.,
The Bolzano-Weierstrass theorem is the jump of weak König’s lemma
. Annals of Pure and Applied Logic, vol. 163 (2012), pp. 623–655.
Brattka, V., Oliva, P., and Pauly, A., On the algebraic structure of Weihrauch degrees, 2013, arXiv:1604.08348.
Buss, S. R. (ed.), Handbook of Proof Theory, Elsevier, Amsterdam, 1998.
Dorais, F. G.,
Classical consequences of continuous choice principles from intuitionistic analysis
. Notre Dame Journal of Formal Logic, vol. 55 (2014), no. 1, pp. 25–39.
Dorais, F. G., Dzhafarov, D. D., Hirst, J. L., Mileti, J. R., and Shafer, P.,
On uniform relationships between combinatorial problems
. Transactions of the American Mathematical Society, vol. 368 (2016), pp. 1321–1359.
Dzhafarov, D. D., Strong reductions between combinatorial principles, this Journal, vol. 81 (2016), no. 4, pp. 1405–1431.
Intuitionistic provability versus uniform provability in RCA
, CiE 2015 (Beckmann, A., Mitrana, V., and Soskova, M., editors), Lecture Notes in Computer Science, vol. 9136, Springer, 2015, pp. 186–195.
Hirst, J. L. and Mummert, C.,
Reverse mathematics and uniformity in proofs without excluded middle
. Notre Dame Journal of Formal Logic, vol. 52 (2011), no. 2, pp. 149–162.
Kleene, S. C., Formalized Recursive Functionals and Formalized Realizability, Memoirs of the American Mathematical Society, vol. 89, American Mathematical Society, Providence, RI, 1969.
Higher order reverse mathematics
, Reverse Mathematics 2001 (Simpson, S. G., editor), Lecture Notes in Logic, vol. 21, A. K. Peters, Wellesley, MA, 2005, pp. 281–295.
Intuitionistic investigations of formalist logic
. Nagoya Mathematical Journal, vol. 2 (1951), pp. 35–47 (in German).
Simpson, S. G., Subsystems of Second Order Arithmetic, Springer-Verlag, New York, NY, 1999.
Troelstra, A. S (ed.), Metamathematical Investigation of Intuitionistic Arithmetic and Analysis, Lecture Notes in Mathematics, vol. 344, Springer, 1973.