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Amalgamation of nonstandard models of arithmetic

Published online by Cambridge University Press:  12 March 2014

Andreas Blass
Andreas Blass*
Affiliation:
University of Michigan, Ann Arbor, Michigan 48109
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Abstract

Any two models of arithmetic can be jointly embedded in a third with any prescribed isomorphic submodels as intersection and any prescribed relative ordering of the skies above the intersection. Corollaries include some known and some new theorems about ultrafilters on the natural numbers, for example that every ultrafilter with the “4 to 3” weak Ramsey partition property is a P-point. We also give examples showing that ultrafilters with the “5 to 4” partition property need not be P-points and that the main theorem cannot be improved to allow a prescribed ordering of lower skies.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 42 , Issue 3 , September 1977 , pp. 372 - 386
Copyright
Copyright © Association for Symbolic Logic 1977

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References

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