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.
Research supported in part by NSF grant MCS76-07163.
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References
J. Barwise,Admissible Sets and Structures, Springer, Berlin, 1975.
J. Barwise and J. Schlipf, ‘An introduction to recursively saturated and resplendent models’J. Symbolic Logic 41 (1976), 531–536.
C. C. Chang and H. J. Keisler, Model Theory, North-Holland, Amsterdam, 1973.
N. Cutland, ‘Π\({\frac{1}{1}}\)-models and ?\({\frac{1}{1}}\)-categoricity’, pp. 42–63 inConference in Mathematical Logic - London’70, Springer Lecture Notes 255
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S. Feferman, ‘A language and axioms for explicit mathematics’, pp. 87-139 in Algebra and Logic, Springer Lecture Notes 450
H. Friedman, ‘Axiomatic recursive function theory’, pp. 113–137 in Logic Colloquium ’ 69, North-Holland, Amsterdam, 1971.
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© 1979 D. Reidel Publishing Company, Dordrecht, Holland
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Feferman, S. (1979). Generalizing Set-Theoretical Model Theory and an Analogue Theory on Admissible Sets. In: Hintikka, J., Niiniluoto, I., Saarinen, E. (eds) Essays on Mathematical and Philosophical Logic. Synthese Library, vol 122. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9825-4_8
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