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Universal structures in power ℵ1

Published online by Cambridge University Press:  12 March 2014

Alan H. Mekler
Alan H. Mekler*
Affiliation:
Department of Mathematics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
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Abstract

It is consistent with ¬ CH that every universal theory of relational structures with the joint embedding property and amalgamation for -(3)-diagrams has a universal model of cardinality ℵ1. For classes with amalgamation for -(4)-diagrams it is consistent that and there is a universal model of cardinality ℵ2.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 55 , Issue 2 , June 1990 , pp. 466 - 477
Copyright
Copyright © Association for Symbolic Logic 1990

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References

REFERENCES

[B]Baumgartner, J., Almost disjoint sets, the dense set problem and the partition calculus, Annals of Mathematical Logic, vol. 9 (1976), pp. 401–439.CrossRefGoogle Scholar
[M]Mekler, A., C.c.c. forcing without combinatorics, this Journal, vol. 49 (1984), pp. 830–832.Google Scholar
[S1]Shelah, S., Independence results, this Journal, vol. 45 (1980), pp. 563–573.Google Scholar
[S2]Shelah, S., On universal graphs without instances of CH, Annals of Pure and Applied Logic, vol. 26 (1984), pp. 75–87.CrossRefGoogle Scholar
[S3]Shelah, S., Universal graphs without instances of CH: revisited, preprint.Google Scholar