zbMATH — the first resource for mathematics

Some open questions for superatomic Boolean algebras. (English) Zbl 1095.03037
Summary: In connection with some known results on uncountable cardinal sequences for superatomic Boolean algebras, we describe some open questions for superatomic Boolean algebras concerning singular cardinals.

03E04 Ordered sets and their cofinalities; pcf theory
06E05 Structure theory of Boolean algebras
Full Text: DOI
[1] Baumgartner, J. E., and S. Shelah, ”Remarks on superatomic Boolean algebras”, Annals of Pure and Applied Logic , vol. 33 (1987), pp. 109–29. · Zbl 0643.03038
[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. · Zbl 0713.03024
[3] Juhász, I., and W. Weiss, ”On thin-tall scattered spaces”, Colloquium Mathematicum , vol. 40 (1978/79), pp. 63–68. · Zbl 0416.54038
[4] Just, W., ”Two consistency results concerning thin-tall Boolean algebras”, Algebra Universalis , vol. 20 (1985), pp. 135–42. · Zbl 0571.03022
[5] Koepke, P., and J. C. Martínez, ”Superatomic Boolean algebras constructed from morasses”, The Journal of Symbolic Logic , vol. 60 (1995), pp. 940–51. JSTOR: · Zbl 0854.06018
[6] Koppelberg, S., Handbook of Boolean Algebras. Vol. 1 , edited by J. D. Monk and R. Bonnet, North-Holland Publishing Co., Amsterdam, 1989. · Zbl 0671.06001
[7] Martínez, J. C., ”A forcing construction of thin-tall Boolean algebras”, Fundamenta Mathematicae , vol. 159 (1999), pp. 99–113. · Zbl 0928.03058
[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 · Zbl 0588.06006
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.