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Power types in explicit mathematics?

Published online by Cambridge University Press:  12 March 2014

Gerhard Jäger*
Affiliation:
Institut Für Informatik und Angewandte Mathematik, Universität Bern, Neubrückstrasse 10, Ch-3012 Bern, Switzerland, E-mail: jaeger@iam.unibe.ch

Abstract

In this note it is shown that in explicit mathematics the strong power type axiom is inconsistent with (uniform) elementary comprehension and discuss some general aspects of power types in explicit mathematics.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1997

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References

REFERENCES

[1]Beeson, M. J., Foundations of constructive mathematics, Springer-Verlag, 1985.CrossRefGoogle Scholar
[2]Feferman, S., A language and axioms for explicit mathematics, Algebra and logic (Crossley, J. N., editor), Lecture Notes in Mathematics, no. 450, Springer-Verlag, 1975.Google Scholar
[3]Feferman, S., Constructive theories of functions and classes, Logic colloquium '78 (Boffa, M., van Dalen, D., and McAloon, K., editors), North-Holland, 1979.Google Scholar
[4]Feferman, S. and Jäger, G., Systems of explicit mathematics with non-constructive μ-operator, Part II, Annals of Pure and Applied Logic, vol. 79 (1996).CrossRefGoogle Scholar
[5]Glass, Th., On power set in explicit mathematics, this Journal, vol. 61 (1996), no. 2, pp. 468489.Google Scholar
[6]Troelstra, A. S. and van Dalen, D., Constructivism in mathematics, vol. I, North-Holland, 1988.Google Scholar