On certain types and models for arithmetic

Journal of Symbolic Logic 39 (1):151-162 (1974)
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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DOI 10.2307/2272355
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L. A. S. Kirby (1984). Ultrafilters and Types on Models of Arithmetic. Annals of Pure and Applied Logic 27 (3):215-252.
James H. Schmerl (1978). Extending Models of Arithmetic. Annals of Mathematical Logic 14 (2):89-109.

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