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Analysis without actual infinity

Published online by Cambridge University Press:  12 March 2014

Jan Mycielski
Jan Mycielski*
Affiliation:
University of Colorado, Boulder, Colorado 80309
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Abstract

We define a first-order theory FIN which has a recursive axiomatization and has the following two properties. Each finite part of FIN has finite models. FIN is strong enough to develop that part of mathematics which is used or has potential applications in natural science. This work can also be regarded as a consistency proof of this hitherto informal part of mathematics. In FIN one can count every set; this permits one to prove some new probabilistic theorems.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 46 , Issue 3 , September 1981 , pp. 625 - 633
Copyright
Copyright © Association for Symbolic Logic 1981

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References

REFERENCES

[0]Barwise, J. (Editor), Handbook of mathematical logic, Springer-Verlag, Berlin and New York, 1978.Google Scholar
[1]Bishop, E., Foundations of constructive analysis, McGraw-Hill, New York, 1967.Google Scholar
[2]J. van Heijenoort, (Editor), From Frege to Gödel, a source book in mathematical logic, Harvard University Press, Cambridge, Massachusetts, 1967.Google Scholar
[3]Mycielski, J., A lattice of interpretability types of theories, this Journal, vol. 42 (1977), pp. 297–305.Google Scholar
[4]Rényi, A., Dialogues on mathematics, Holden-Day, San Francisco. 1967.Google Scholar
[5]Robinson, A., Formalism 64, Logic, Methodology and Philosophy of Science, Proceedings of the 1964 Congress in Jerusalem, (Hillel, Y. Bar, Editor), North-Holland, Amsterdam, 1965, pp. 228–246.Google Scholar
[6]Tarski, A., Mostowski, A. and Robinson, R.M., Undecidable theories, North-Holland, Amsterdam, 1953.Google Scholar
[7]Ulam, S.M., Sels, numbers and universes, MIT Press, Cambridge, Massachusetts, 1974, pp. 164–210 (reproduced from Annals of Mathematics, vol. 42 (1941), pp. 874–920).Google Scholar
[8]Yessenin-Volpin, A. S., The ultra-intuitionistic criticism and the antitraditional program for foundations of mathematics, Intuitionism and proof theory, Proceedings of the Summer Conference at Buffalo, New York, 1968, North-Holland, Amsterdam, 1970.Google Scholar
[9]Parikh, R., Existence and feasibility in arithmetic, this Journal, vol. 36 (1971), pp. 494–508.Google Scholar