Notre Dame Journal of Formal Logic

Some Open Questions for Superatomic Boolean Algebras

Juan Carlos Martínez

Abstract

In connection with some known results on uncountable cardinal sequences for superatomic Boolean algebras, we shall describe some open questions for superatomic Boolean algebras concerning singular cardinals.

Article information

Source
Notre Dame J. Formal Logic Volume 46, Number 3 (2005), 353-356.

Dates
First available: 30 August 2005

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1125409333

Digital Object Identifier
doi:10.1305/ndjfl/1125409333

Zentralblatt MATH identifier
05011398

Mathematical Reviews number (MathSciNet)
MR2162105

Subjects
Primary: 03E75: Applications of set theory 06E05: Structure theory
Secondary: 03E04: Ordered sets and their cofinalities; pcf theory

Keywords
superatomic Boolean algebra cardinal sequence

Citation

Martínez, Juan Carlos. Some Open Questions for Superatomic Boolean Algebras. Notre Dame Journal of Formal Logic 46 (2005), no. 3, 353--356. doi:10.1305/ndjfl/1125409333. http://projecteuclid.org/euclid.ndjfl/1125409333.


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References

  • [1] Baumgartner, J. E., and S. Shelah, "Remarks on superatomic Boolean algebras", Annals of Pure and Applied Logic, vol. 33 (1987), pp. 109--29.
  • [2] Burke, M. R., and M. Magidor, "Shelah's pcf theory and its applications", Annals of Pure and Applied Logic, vol. 50 (1990), pp. 207--54.
  • [3] Juhász, I., and W. Weiss, "On thin-tall scattered spaces", Colloquium Mathematicum, vol. 40 (1978/79), pp. 63--68.
  • [4] Just, W., "Two consistency results concerning thin-tall Boolean algebras", Algebra Universalis, vol. 20 (1985), pp. 135--42.
  • [5] Koepke, P., and J. C. Martínez, "Superatomic Boolean algebras constructed from morasses", The Journal of Symbolic Logic, vol. 60 (1995), pp. 940--51.
  • [6] Koppelberg, S., Handbook of Boolean Algebras. Vol. 1, edited by J. D. Monk and R. Bonnet, North-Holland Publishing Co., Amsterdam, 1989.
  • [7] Martínez, J. C., "A forcing construction of thin-tall Boolean algebras", Fundamenta Mathematicae, vol. 159 (1999), pp. 99--113.
  • [8] Ruyle, J., Cardinal Sequences of PCF Structures, Ph.D. thesis, University of California, Riverside, 1998.
  • [9] Weese, M., "On cardinal sequences of Boolean algebras", Algebra Universalis, vol. 23 (1986), pp. 85--97. špace-2\baselineskip