Journal of Symbolic Logic

On Certain Types and Models for Arithmetic

Andreas Blass

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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.

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

First available in Project Euclid: 6 July 2007

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Blass, Andreas. On Certain Types and Models for Arithmetic. J. Symbolic Logic 39 (1974), no. 1, 151--162.

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