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On certain types and models for arithmetic

Published online by Cambridge University Press:  12 March 2014

Andreas Blass
Andreas Blass*
Affiliation:
University of Michigan, Ann Arbor, Michigan 48104
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Abstract

There is an analogy between concepts such as end-extension types and minimal types in the model theory of Peano arithmetic and concepts such as P-points and selective ultrafilters in the theory of ultrafilters on N. Using the notion of conservative extensions of models, we prove some theorems clarifying the relation between these pairs of analogous concepts. We also use the analogy to obtain some model-theoretic results with techniques originally used in ultrafilter theory. These results assert that every countable nonstandard model of arithmetic has a bounded minimal extension and that some types in arithmetic are not 2-isolated.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 39 , Issue 1 , March 1974 , pp. 151 - 162
Copyright
Copyright © Association for Symbolic Logic 1974

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References

BIBLIOGRAPHY

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