Amalgamation of nonstandard models of arithmetic

Journal of Symbolic Logic 42 (3):372-386 (1977)
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
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    Citations of this work BETA
    Andreas Blass (1988). Selective Ultrafilters and Homogeneity. Annals of Pure and Applied Logic 38 (3):215-255.
    Michael Canjar (1988). Countable Ultraproducts Without CH. Annals of Pure and Applied Logic 37 (1):1-79.
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