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A note on exponentiation

Published online by Cambridge University Press:  12 March 2014

Ch. Cornaros  and
C. Dimitracopoulos
Ch. Cornaros
Affiliation:
Department of Mathematics, University of Crete, 714 09 Iraklio, Greece, E-mail: kornaros@talos.cc.uch.gr
C. Dimitracopoulos
Affiliation:
Department of Mathematics, University of Crete, 714 09 Iraklio, Greece, E-mail: cdimitr@grearn.bitnet
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Abstract

We study the strength (over bounded induction) of axioms expressing particular cases of the Chinese Remainder Theorem with respect to the axiom ∀x, y∃z (z = xy).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 58 , Issue 1 , March 1993 , pp. 64 - 71
Copyright
Copyright © Association for Symbolic Logic 1993

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References

REFERENCES

[1]D'Aquino, P., Local behavior of the Chebyshev theorem in models of IΔ0, this Journal, vol. 57(1992), pp. 12–27.Google Scholar
[2]Dimitracopoulos, C., Matijasevič's theorem and fragments of arithmetic. Ph.D. thesis, University of Manchester, 1980.Google Scholar
[3]Dimitracopoulos, C. and Paris, J., The pigeonhole principle and fragments of arithmetic, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 32 (1986), pp. 73–80.CrossRefGoogle Scholar
[4]Kaye, R., Diophantine induction, Annals of Pure and Applied Logic, vol. 46 (1990), pp. 1–40.CrossRefGoogle Scholar
[5]Paris, J. and Kirby, L. A. S., ∑n-collection schemes in arithmetic, Logic colloquium '77, North-Holland, Amsterdam, 1978, pp. 199–209.CrossRefGoogle Scholar
[6]Paris, J. B., Wilke, A. J., and Woods, A. R., Provability of the pigeonhold principle and the existence of infinitely many primes, this Journal, vol. 53 (1988), pp. 1235–1244.Google Scholar
[7]Woods, A. R., Some problems in logic and number theory, and their connections, Ph.D. thesis, University of Manchester, 1981.Google Scholar