Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-26T12:30:46.515Z Has data issue: false hasContentIssue false

On classes closed under unions of chains

Published online by Cambridge University Press:  12 March 2014

Douglas E. Miller*
Affiliation:
Yale University, New Haiven, Connecticut 06520
*
University of Illinois at Chicago Circle, Chicago, IL 60680

Abstract

We improve a general theorem of J. A. Makowsky which characterizes, for a wide class of languages, those sentences θ such that both Mod(θ) and Mod(¬θ) are closed under unions of chains.

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]Addison, J. W., Some problems in hierarchy theory, Proceedings of Symposia in Pure Mathematics, vol. 5, American Mathematical Society, Providence, 1962, pp. 123130.Google Scholar
[2]Miller, D. E., The invariant Πα0 separation principle, Transactions of the American Mathematical Socity, vol. 242 (1978), pp. 185205.Google Scholar
[3]Makowsky, J. A., Securable quantifiers, n-unions and admissible sets, Logic Colloquium '73 (Rose, , Editor), North-Holland, Amsterdam, 1975, pp. 409428.Google Scholar
[4]Nebres, B. F., Infinitary formulas preserved under unions of models, this Journal, vol. 37 (1972), pp. 449466.Google Scholar
[5]Weinstein, J. M., 1, ω) properties of unions of models, The syntax and semantics of infinitary languages (Barwise, J., Editor), Springer-Verlag, Berlin and New York, 1968, pp. 265268.CrossRefGoogle Scholar