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Superatomic Boolean algebras constructed from morasses

Published online by Cambridge University Press:  12 March 2014

Peter Koepke  and
Juan Carlos Martínez
Peter Koepke
Affiliation:
Mathematisches Institut, Beringstrasse 4, D-5300 Bonn 1, Germany
Juan Carlos Martínez
Affiliation:
Facultad De Matemáticas, Universidad De Barcelona, Gran Vía 585, 08007 Barcelona, Spain
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Abstract

By using the notion of a simplified (κ, 1)-morass, we construct κ-thin-tall, κ-thin-thick and, in a forcing extension, κ-very thin-thick superatomic Boolean algebras for every infinite regular cardinal κ.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 60 , Issue 3 , September 1995 , pp. 940 - 951
Copyright
Copyright © Association for Symbolic Logic 1995

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References

REFERENCES

[1]Baumgartner, J. E. and Shelah, S., Remarks on superatomic Boolean algebras, Annals of Pure and Applied Logic, vol. 33 (1987), pp. 109–129.CrossRefGoogle Scholar
[2]Devlin, K. J., Constructibility, Springer-Verlag, Berlin, 1984.CrossRefGoogle Scholar
[3]Jech, T., Set theory, Academic Press, New York, 1978.Google Scholar
[4]Juhász, I. and Weiss, W., On thin-tall scattered spaces, Colloquium Mathematicum, vol. 40 (1978), pp. 63–68.CrossRefGoogle Scholar
[5]Kunen, K., Set theory, North-Holland, Amsterdam, 1980.Google Scholar
[6]Martínez, J. C., A consistency result on thin-tall superatomic Boolean algebras, Proceedings of the American Mathematical Society, vol. 115 (1992), pp. 473–477.CrossRefGoogle Scholar
[7]Roitman, J., Height and width of superatomic Boolean algebras, Proceedings of the American Mathematical Society, vol. 94 (1985), pp. 9–14.CrossRefGoogle Scholar
[8]Roitman, J., A very thin thick superatomic Boolean algebra, Algebra Universalis, vol. 21 (1985), pp. 137–142.CrossRefGoogle Scholar
[9]Roitman, J., Superatomic Boolean algebras, Handbook of Boolean algehras(Monk, J. D. and Bonnet, R., editors), North-Holland, Amsterdam, 1989, pp. 719–740.Google Scholar
[10]Velleman, D. J., ω-morasses, and a weak form of Martin's axiom provable in ZFC, Transactions of the American Mathematical Society, vol. 285 (1984),pp. 617–627.Google Scholar
[11]Velleman, D. J., Simplified morasses, this Journal, vol. 49 (1984), pp. 257–271.Google Scholar
[12]Weese, M., On cardinal sequences of Boolean algebras, Algebra Universalis, vol. 23 (1986), pp. 85–97.CrossRefGoogle Scholar