Notre Dame Journal of Formal Logic

Some Open Questions for Superatomic Boolean Algebras

Juan Carlos Martínez


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

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

First available in Project Euclid: 30 August 2005

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

superatomic Boolean algebra cardinal sequence


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

Export citation


  • [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