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Nonstandard set theory

Published online by Cambridge University Press:  12 March 2014

Peter Fletcher
Peter Fletcher*
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW, England
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Abstract

Nonstandard set theory is an attempt to generalise nonstandard analysis to cover the whole of classical mathematics. Existing versions (Nelson, Hrbáček, Kawai) are unsatisfactory in that the unlimited idealisation principle conflicts with the wish to have a full theory of external sets.

I re-analyse the underlying requirements of nonstandard set theory and give a new formal system, stratified nonstandard set theory, which seems to meet them better than the other versions.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 54 , Issue 3 , September 1989 , pp. 1000 - 1008
Copyright
Copyright © Association for Symbolic Logic 1989

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References

REFERENCES

[0]Bernstein, A. R., Non-standard analysis, Studies in model theory (Morley, M. D., editor), Studies in Mathematics, vol. 8, Mathematical Association of America, Buffalo, New York, 1973, pp. 35–58.Google Scholar
[1]Fletcher, P., Nonstandard set theory, M.Sc. thesis, University of Bristol, Bristol, 1987.Google Scholar
[2]Hrbáček, K., Axiomatic foundations for nonstandard analysis, Fundamenta Mathematicae, vol. 98 (1978), pp. 1–19.CrossRefGoogle Scholar
[3]Kawai, T., Nonstandard analysis by axiomatic method, Proceedings of Southeast Asian conference on logic (Singapore, 1981), Studies in Logic and the Foundations of Mathematics, vol. 111, North-Holland, Amsterdam, 1983, pp. 55–76.CrossRefGoogle Scholar
[4]Nelson, E., Internal set theory: a new approach to nonstandard analysis, Bulletin of the American Mathematical Society, vol. 83 (1977), pp. 1165–1198.CrossRefGoogle Scholar
[5]Robinson, A., Nonstandard analysis, North-Holland, Amsterdam, 1966.Google Scholar
[6]Robinson, A. and Zakon, E., A set-theoretical characterisation of enlargements, Applications of model theory to algebra, analysis and probability (Luxemburg, W. A. J., editor), Holt, Rinehart and Winston, New York, 1969, pp. 109–122.Google Scholar