Hostname: page-component-7c8c6479df-7qhmt Total loading time: 0 Render date: 2024-03-29T07:04:13.249Z Has data issue: false hasContentIssue false

LA(Ⅎ)

Published online by Cambridge University Press:  12 March 2014

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

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
Copyright
Copyright © Association for Symbolic Logic 1979

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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. 225265.CrossRefGoogle Scholar
[3]Chang, C. C. and Keisler, H. J., Model theory North-Holland, Amsterdam, 1973.Google Scholar
[4]Keisler, H. J., Logic with the quantifier ‘there exist uncountably many’, Annals of Mathematical Logic, vol. 1 (1970), pp. 193.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[5]Keisler, H. J., LA(Q), mimeographed, 1970 (unpublished).Google Scholar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