Generalizing Set-Theoretical Model Theory and an Analogue Theory on Admissible Sets

  • Solomon Feferman
Part of the Synthese Library book series (SYLI, volume 122)

Abstract

By set-theoretical model theory I mean the kind of model theory for finitary first order predicate calculus L ω,ω exemplified by the book by Chang and Keisler [C, K]. As we know, parts of this (such as the completeness theorem) can be carried out in a completely elementary framework. The distinctively set-theoretical parts of [C, K] use the theory of transfinite ordinals and cardinals, the axiom of choice and, on occasion, the continuum hypothesis and its generalizations.

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References

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    J. Barwise,Admissible Sets and Structures, Springer, Berlin, 1975.Google Scholar
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    J. Barwise and J. Schlipf, ‘An introduction to recursively saturated and resplendent models’J. Symbolic Logic 41 (1976), 531–536.CrossRefGoogle Scholar
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    C. C. Chang and H. J. Keisler, Model Theory, North-Holland, Amsterdam, 1973.Google Scholar
  4. [CI]
    N. Cutland, ‘Π\({\frac{1}{1}}\)-models and ?\({\frac{1}{1}}\)-categoricity’, pp. 42–63 inConference in Mathematical Logic - London70, Springer Lecture Notes 255Google Scholar
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    N. Cutland, Model theory on admissible sets, Annals Math. Logic 5 (1973), 257–289.CrossRefGoogle Scholar
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    S. Feferman, ‘A language and axioms for explicit mathematics’, pp. 87-139 in Algebra and Logic, Springer Lecture Notes 450Google Scholar
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    H. Friedman, ‘Axiomatic recursive function theory’, pp. 113–137 in Logic Colloquium 69, North-Holland, Amsterdam, 1971.Google Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1979

Authors and Affiliations

  • Solomon Feferman
    • 1
  1. 1.Department of MathematicsStanford UniversityUSA

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