## Journal of Symbolic Logic

### On Certain Types and Models for Arithmetic

Andreas Blass

#### 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.

#### Article information

Source
J. Symbolic Logic, Volume 39, Issue 1 (1974), 151-162.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183738960

Mathematical Reviews number (MathSciNet)
MR369050

Zentralblatt MATH identifier
0296.02031

JSTOR