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A note on subsystems of open induction

Published online by Cambridge University Press:  12 March 2014

Shahram Mohsenipour
Shahram Mohsenipour*
Affiliation:
Institute for Studies in Theoretical Physics and Mathematics, P.O. BOX 19395-5746, Tehran, Iran. E-mail: [email protected]
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Abstract

We completely characterize the logical hierarchy of subsystems of open induction introduced by Boughattas [1].

Keywords

Open inductionsubsystemGalios theory
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 4 , December 2007 , pp. 1318 - 1322
Copyright
Copyright © Association for Symbolic Logic 2007

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References

REFERENCES

[1]Boughattas, Sedki, L'arithmétique ouverte et ses modèles non-standards, this Journal, vol. 56 (1991), no. 2, pp. 700–714.Google Scholar
[2]Boughattas, Sedki, L'induction ouverte dans les anneaux discrets ordonnés et normaux n'est pas finiment axiomatisable, Journal of the London Mathematical Society. Second Series, vol. 53 (1996), no. 3, pp. 455–463.CrossRefGoogle Scholar
[3]Jacobson, Nathan, Basic algebra, I, second ed., W. H. Freeman and Company, New York, 1985.Google Scholar
[4]Malle, Gunter and Matzat, B. Heinrich, Inverse Galois theory, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 1999.CrossRefGoogle Scholar
[5]Shepherdson, J. C., A non-standard model for a free variable fragment of number theory, Bulletin de l'Académie Polonaise des Sciences, vol. 12 (1964), pp. 79–86.Google Scholar