## Journal of Symbolic Logic

### Amalgamation of Nonstandard Models of Arithmetic

Andreas Blass

#### 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.

#### Article information

Source
J. Symbolic Logic, Volume 42, Issue 3 (1977), 372-386.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183740012

Mathematical Reviews number (MathSciNet)
MR469750

Zentralblatt MATH identifier
0381.03050

JSTOR

#### Citation

Blass, Andreas. Amalgamation of Nonstandard Models of Arithmetic. J. Symbolic Logic 42 (1977), no. 3, 372--386. https://projecteuclid.org/euclid.jsl/1183740012