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Saturated models of Peano arithmetic

Published online by Cambridge University Press:  12 March 2014

J. F. Pabion
J. F. Pabion*
Affiliation:
Université Claude Bernard-Lyon 1, 69622 Villeurbanne Cedex, France
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Abstract

We study reducts of Peano arithmetic for which conditions of saturation imply the corresponding conditions for the whole model. It is shown that very weak reducts (like pure order) have such a property for κ-saturation in every κ ≥ ω1. In contrast, other reducts do the job for ω and not for κ > ω1. This solves negatively a conjecture of Chang.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 47 , Issue 3 , September 1982 , pp. 625 - 637
Copyright
Copyright © Association for Symbolic Logic 1982

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References

REFERENCES

[1]Chang, C. C. and Keisler, H. J., Model theory, North-Holland, Amsterdam, 1973.Google Scholar
[2]Lucas, F., Thèse de 3® Cycle, Université de Paris VII, Paris.Google Scholar
[3]Richard, D., Thèse de 3® Cycle, Université Claude-Bernard-Lyon, 1979.Google Scholar
[4]Shoenfield, R., Mathematical logic, Addison-Wesley, Reading, Mass., 1967.Google Scholar