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On quantification with a finite universe

Published online by Cambridge University Press:  12 March 2014

Saharon Shelah*
Affiliation:
Institute of Mathematics, The Hebrew University, Jerusalem, Israel Rutgers University, Mathematics Department, New Brunswick, New Jersey, USA

Abstract

We consider a finite universe (more exactly—a family of them), second order quantifiers QK, where for each this means quantifying over a family of n(K)-place relations closed under permuting . We define some natural orders and shed some light on the classification problem of those quantifiers.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2000

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References

[1]Baldwin, John T., Definable second order quantifiers, Model theoretic logics (Barwise, J. and Feferman, S., editors), Perspectives in Mathematical Logic, Springer-Verlag, New York, Berlin, Heidelberg, and Tokyo, 1985, pp. 446–478.Google Scholar
[2]Baldwin, John T. and Shelah, Saharon, Second-order quantifiers and the complexity of theories, Notre Dame Journal of Formal Logic, vol. 26 (1985), pp. 229–303, Proceedings of the 1980/1 Jerusalem Model Theory year.CrossRefGoogle Scholar
[3]Shelah, Saharon, Non-structure theory, accepted, Oxford University Press.Google Scholar
[4]Shelah, Saharon, On quantification with a finite universe II.Google Scholar
[5]Shelah, Saharon, There are just four second-order quantifiers, Israel Journal of Mathematics, vol. 15 (1973), pp. 282–300.CrossRefGoogle Scholar
[6]Shelah, Saharon, Classifying of generalized quantifiers, Around classification theory of models, Lecture Notes in Mathematics, no. 1182, Springer-Verlag, Berlin, 1986, pp. 1–46.CrossRefGoogle Scholar

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