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LA(Ⅎ)

Published online by Cambridge University Press:  12 March 2014

Kim Bruce  and
H. J. Keisler
Kim Bruce
Affiliation:
University of Wisconsin, Madison, Wisconsin 53706
H. J. Keisler*
Affiliation:
Princeton University, Princeton, New Jersey 08540
*
Williams College, Williamstown, Massachusetts 01267
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Abstract

The language LA(Ⅎ) is formed by adding the quantifier Ⅎx, “few x”, to the infinitary logic LA on an admissible set A. A complete axiomatization is obtained for models whose universe is the set of ordinals of A and where Ⅎx is interpreted as there exist A-finitely many x. For well-behaved A, every consistent sentence has a model with an A-recursive diagram. A principal tool is forcing for LA(Ⅎ).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 44 , Issue 1 , March 1979 , pp. 15 - 28
Copyright
Copyright © Association for Symbolic Logic 1979

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References

BIBLIOGRAPHY

[1]Barwise, Jon, Admissible sets and structures, Springer-Verlag, Berlin and New York, 1975.CrossRefGoogle Scholar
[2]Bruce, Kim B., Model-theoretic forcing in logic with a generalized quantifier, Annals of Mathematical Logic, vol. 13 (1978), pp. 225–265.CrossRefGoogle Scholar
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[4]Keisler, H. J., Logic with the quantifier ‘there exist uncountably many’, Annals of Mathematical Logic, vol. 1 (1970), pp. 1–93.CrossRefGoogle Scholar
[5]Keisler, H. J., LA(Q), mimeographed, 1970 (unpublished).Google Scholar
[6]Keisler, H. J., Model theory for infinitary logic, North-Holland, Amsterdam, 1971.Google Scholar