Journal of Symbolic Logic

On Certain Types and Models for Arithmetic

Andreas Blass

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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.

Article information

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

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183738960

Mathematical Reviews number (MathSciNet)
MR369050

Zentralblatt MATH identifier
0296.02031

JSTOR
links.jstor.org

Citation

Blass, Andreas. On Certain Types and Models for Arithmetic. J. Symbolic Logic 39 (1974), no. 1, 151--162. https://projecteuclid.org/euclid.jsl/1183738960


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