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The axiom of choice and combinatory logic

Published online by Cambridge University Press:  12 March 2014

Andrea Cantini
Andrea Cantini*
Affiliation:
Dipartimento di Filosofia, Università Degli Studi di Firenze, Firenze, Italy, E-mail: cantini@philos.unifi.it
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Abstract

We combine a variety of constructive methods (including forcing, realizability, asymmetric interpretation), to obtain consistency results concerning combinatory logic with extensionality and (forms of) the axiom of choice.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 68 , Issue 4 , December 2003 , pp. 1091 - 1108
Copyright
Copyright © Association for Symbolic Logic 2003

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References

REFERENCES

[1] Avigad, J., Interpreting classical theories in constructive ones, this Journal, vol. 65 (2000), pp. 1785–1812.Google Scholar
[2] Barendregt, H., Combinatory logic and the axiom of choice, Indagationes Mathematicae, vol. 35 (1973), pp. 203–221.Google Scholar
[3] Barendregt, H., The lambda calculus. Its syntax and semantics, Studies in Logic and the Foundations of Mathematics, Elsevier, Amsterdam, 1984.Google Scholar
[4] Beeson, M. J., Foundations of constructive mathematics, Springer-Verlag, Berlin, 1985.CrossRefGoogle Scholar
[5] Boffa, M., van Dalen, D., and McAloon, K. (editors), Logic colloquium '78, Studies in Logic and the Foundations of Mathematics, North-Holland, Amsterdam, 1979.Google Scholar
[6] Buss, S. J., Bounded arithmetic, Bibliopolis, Napoli, 1986.Google Scholar
[7] Cantini, A., Notes on formal theories of truth, Zeitschrift für Mathematische Logik unddie Grund-lagen der Mathematik, vol. 35 (1989), pp. 97–130.Google Scholar
[8] Cantini, A., Choice and uniformity in weak applicative theories, Logic Colloquium 2001, Wien, to appear.Google Scholar
[9] Coquand, T. and Hofmann, M., A new method for establishing conservativity of classical systems over their intuitionistic version, Mathematical Structures in Computer Science, vol. 9 (1999), pp. 323–333.Google Scholar
[10] Crossley, J. N. (editor), Algebra and logic, Lecture Notes in Mathematics, vol. 450, Springer-Verlag, Berlin, 1975.Google Scholar
[11] Feferman, S., A language and axioms for explicit mathematics, in [10], pp. 87–139, 1975.Google Scholar
[12] Feferman, S., Constructive theories of functions and classes, in [5], pp. 159–225, 1979.Google Scholar
[13] Ferreira, F., Polynomial time computable arithmetic, in [16], pp. 147–156, 1990.Google Scholar
[14] Goernemann, S., A logic stronger than intuitionism, this Journal, vol. 36 (1971), pp. 249–261.Google Scholar
[15] Minari, P., Theories with types and names with positive stratified comprehension, Studio Logica, vol. 62 (1999), pp. 215–242.Google Scholar
[16] Sieg, W. (editor), Logic and computation, Contemporary Mathematics, American Mathematical Society, Providence, R. I., 1990.CrossRefGoogle Scholar
[17] Troelstra, A. S. and Schwichtenberg, H., Basic proof theory, Cambridge University Press, 1997.Google Scholar
[18] Troelstra, A. S. and van Dalen, D., Constructivism in mathematics, Studies in Logic and the Foundations of Mathematics, Elsevier-North Holland, Amsterdam, 1988.Google Scholar