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Axiomatizing universal properties of quantifiers

Published online by Cambridge University Press:  12 March 2014

Kees Doets*
Affiliation:
Department of Mathematics and Computer Science, University of Amsterdam, 1018 TV Amsterdam, The Netherlands

Abtract

We axiomatize all quantifier properties which can be expressed by a universal condition on the class of algebras of sets.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1991

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References

REFERENCES

Barwise, J. [1978], Monotone quantifiers and admissible sets, Generalized recursion theory. II (Fenstad, J. E. et al., editors), North-Holland, Amsterdam, pp. 138.Google Scholar
Bruce, K. [1978], Ideal models and some not so ideal problems in the model theory of L(Q), this Journal, vol. 43, pp. 304321.Google Scholar
Chang, C. C. and Keisler, H. J. [1973], Model theory, North-Holland, Amsterdam.Google Scholar
van der Does, J., [199?], A generalized quantifier logic for naked infinitives, Language and Philosophy (to appear) (see the Appendix).Google Scholar
van Lambalgen, M. [1990], The axiomatization of randomness, this Journal, vol. 55, pp. 11431167.Google Scholar
Makowsky, J. A. and Tulipani, S. [1976], Some model theory for monotone quantifiers, Archiv für Mathematische Logik und Grundlagenforschung, vol. 18, pp. 115134.CrossRefGoogle Scholar
Westerståhl, D. [1989], Quantifiers in formal and natural languages, Handbook of philosophical logic. Vol. IV (Gabbay, D. and Guenthner, F., editors), Reidel, Dordrecht, pp. 1131 (see Appendix B).Google Scholar