Skip to main content Accessibility help
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 16
  • Print publication year: 2005
  • Online publication date: March 2017

Higher order reversemathematics

[1] J., Avigad and S., Feferman, Gödel's functional (‘Dialectica’) interpretation, [3], 1998, pp. 337–405.
[2] M. J., Beeson, Foundations of constructive mathematics, Springer Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge, Bd. 6., Berlin Heidelberg, New York, Tokyo, 1985.
[3] S. R., Buss (editor), Handbook of proof theory, Studies in Logic and the Foundations of Mathematics, vol. 137, Elsevier, 1998.
[4] S., Feferman, Theories of finite type related to mathematical practice,Handbook of mathematical logic (J., Barwise, editor), North-Holland, Amsterdam, 1977, pp. 913–972.
[5] U., Felgner, Models of ZF–set theory, Lecture Notes in Mathematics, vol. 223, Springer, Berlin, 1971.
[6] H., Friedman, Systems of second order arithmetic with restricted induction (abstract),The Journal of Symbolic Logic, vol. 41 (1976), pp. 558–559.
[7] Kurt, Gödel, Über eine bisher noch nicht benützte Erweiterung des finiten Standpunktes,Dialectica, vol. 12 (1958), pp. 280–287.
[8] T. J., Grilliot, On effectively discontinuous type-2 objects,The Journal of Symbolic Logic, vol. 36 (1971), pp. 245–248.
[9] S. C., Kleene, Recursive functionals and quantifiers of finite types I,Transactions of the American Mathematical Society, vol. 91 (1959), pp. 1–52.
[10] U., Kohlenbach, Effective moduli from ineffective uniqueness proofs. an unwinding of de la Vallee Poussin's proof for Chebycheff approximation,Annals of Pure and Applied Logic, vol. 64 (1993), pp. 27–94.
[11] U., Kohlenbach, Proof theory and computational analysis, Electronic Notes in Theoretical Computer Science, vol. 13, Elsevier, 1998. [12],Things that can and things that can't be done in PRA,Annals of Pure and Applied Logic, vol. 102 (2000), pp. 223–245.
[13] U., Kohlenbach, Foundational and mathematical uses of higher types,Reflections on the Foundations of Mathematics: Essays in Honor of Solomon Feferman, Lecture Notes in Logic, vol. 15, A.K. Peters, 2002, pp. 92–116.
[14] U., Kohlenbach, On uniform weak König's lemma,Annals of Pure and Applied Logic, vol. 114 (2002), pp. 103–116.
[15] N., Shioji and K., Tanaka, Fixed point theory in weak second-order arithmetic,Annals of Pure and Applied Logic, vol. 47 (1990), pp. 167–188.
[16] S.G., Simpson, Subsystems of second order arithmetic, Perspectives inMathematical Logic, Springer-Verlag, 1999.
[17] A. S., Troelstra (editor), Metamathematical investigation of intuitionistic arithmetic and analysis, Lecture Notes in Mathematics, vol. 344, Springer, 1973.
[18] A. S., Troelstra, Note on the fan theorem,The Journal of Symbolic Logic, vol. 39 (1974), pp. 584– 596.
[19] A. S., Troelstra and D., van Dalen, Constructivism in mathematics, vol. II, Noth-Holland, 1988.
[20] K., Weihrauch, Computable analysis, Springer, Berlin, 2000.