Brown, Douglas K., Notions of compactness in weak subsystems of second order arithmetic, Reverse mathematics 2001 (Simpson, S.G., editor), Lecture Notes in Logic, vol. 21, Association for Symbolic Logic, La Jolla, CA, 2005, pp. 47–66.
Ferreira, Fernando and Oliva, Paulo, Bounded functional interpretation, Annals of Pure and Applied Logic, vol. 135 (2005), pp. 73–112.
Hirst, Jeffry L., Combinatorics in subsystems of second order arithmetic, Ph.D. thesis, Pennsylvania State University, 1987.
Kohlenbach, Ulrich, Mathematically strong subsystems of analysis with low rate of growth of provably recursive functionals, Archive for Mathematical Logic, vol. 36 (1996), pp. 31–71.
Kohlenbach, Ulrich, Arithmetizing proofs in analysis, Logic Colloquium '96 (San Sebastián) (Larrazabal, J.M., Lascar, D., and Mints, G., editors), Springer Lecture Notes Logic, vol. 12, Springer, Berlin, 1998, pp. 115–158.
Kohlenbach, Ulrich, Foundational and mathematical uses of higher types, Reflections on the foundations of mathematics: Essays in Honor of Solomon Feferman (Sieg, W.
et al., editors), Lecture Notes in Logic, vol. 15, Association for Symbolic Logic, Urbana, IL, 2002, pp. 92–116.
Kohlenbach, Ulrich, A logical uniform boundedness principle for abstract metric and hyperbolic spaces, Proceedings of the 13th Workshop on Logic, Language, Information and Computation (WoLLIC 2006), Electronic Notes in Theoretical Computer Science, vol. 165, Elsevier Sci. B. V., Amsterdam, 2006, pp. 81–93.
Kohlenbach, Ulrich, Applied proof theory: proof interpretations and their use in mathematics, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2008.
Simpson, Stephen G., Subsystems of second order arithmetic, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1999.
Tao, Terence, Soft analysis, hardanalysis, and thefinite convergence principle, http://terrytao.wordpress.com, 2007, Appeared in “T. Tao, Structure and Randomness: Pages from Year One of a Mathematical Blog, American Mathematical Society, pp. 298, 2008.”.
Troelstra, A. S. and van Dalen, D., Constructivism in mathematics. Vol. I and II, North-Holland Publishing Co., Amsterdam, 1988.