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Full Satisfaction Classes and Recursive Saturation

Published online by Cambridge University Press:  20 November 2018

A. H. Lachlan
A. H. Lachlan*
Affiliation:
Simon Fraser UniversityBurnaby 2, B.C. V5A 1S6
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Abstract

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It is shown that a nonstandard model of Peano arithmetic which has a full satisfaction class is necessarily recursively saturated.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 3 , 01 September 1981 , pp. 295 - 297
Copyright
Copyright © Canadian Mathematical Society 1981

References

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2. Krajewski, S.. Non-standard satisfaction classes. Set Theory and Hierarchy Theory, Lecture Notes in Mathematics vol. 537, Springer, Berlin 1976, pp. 121-145.Google Scholar
3. MacDowell, R. and Specker, E., Modelle der Arithmetik, Infinitistic Methods, Panstwowe Wydawnictwo Naukowe, Warsaw 1961, pp. 257-263.Google Scholar
4. Schlipf, J.. Toward model theory through recursive saturation, J. Symb. Logi. 43 (1978), pp. 183-203.Google Scholar