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Nonstandard characterizations of recursive saturation and resplendency

Published online by Cambridge University Press:  12 March 2014

Stuart T. Smith
Stuart T. Smith*
Affiliation:
Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada Department of Mathematics and Computer Science, Ben-Gurion University of the Negev, Beersheva, Israel
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Abstract

We prove results about nonstandard formulas in models of Peano arithmetic which complement those of Kotlarski, Krajewski, and Lachlan in [KKL] and [L]. This enables us to characterize both recursive saturation and resplendency in terms of statements about nonstandard sentences. Specifically, a model of PA is recursively saturated iff is nonstandard and -logic is consistent. is resplendent iff is nonstandard, -logic is consistent, and every sentence φ which is consistent in -logic is contained in a full satisfaction class for . Thus, for models of PA, recursive saturation can be expressed by a (standard) -sentence and resplendency by a -sentence.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 52 , Issue 3 , September 1987 , pp. 842 - 863
Copyright
Copyright © Association for Symbolic Logic 1987

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Footnotes

1

The author acknowledges support of NSERC grant no. 5403.

References

REFERENCES

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