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Generalized prime models

Published online by Cambridge University Press:  12 March 2014

Robert Fittler
Robert Fittler*
Affiliation:
Universität Zurich, Zurich, Switzerland
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Extract

A prime model O of some complete theory T is a model which can be elementarily imbedded into any model of T (cf. Vaught [7, Introduction]). We are going to replace the assumption that T is complete and that the maps between the models of T are elementary imbeddings (elementary extensions) by more general conditions. T will always be a first order theory with identity and may have function symbols. The language L(T) of T will be denumerable. The maps between models will be so called F-maps, i.e. maps which preserve a certain set F of formulas of L(T) (cf. I.1, 2). Roughly speaking a generalized prime model of T is a denumerable model O which permits an F-map O→M into any model M of T. Furthermore O has to be “generated” by formulas which belong to a certain subset G of F.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 36 , Issue 4 , December 1971 , pp. 593 - 606
Copyright
Copyright © Association for Symbolic Logic 1972

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References

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