Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-24T02:02:44.338Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
C. Dimitracopoulos
Affiliation:
Department of Mathematics, University of Crete, 714 09 Iraklio, Greece, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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