Cardinal Invariants on Boolean Algebras
J. Donald Monk, University of Colorado
ISBN 3-7643-5402-X, Published 1996, Hardcover, 312 pages
Series: Progress in Mathematics, Volume 142
Birkhäuser Boston [We thank Birkhäuser for permission to reprint material contained in this book.]
The purpose of these notes is to describe the progress made on the 97 open problems formulated in the book Cardinal invariants on Boolean algebras, Although we assume acquaintance with that book, we give some background for many problems, and state without proof most results relevant to the problems, as far as the author knows. Many of the problems have been solved, at least partially, by Saharon Shelah. For the unpublished papers of Shelah mentioned in the references, see his archive, which can currently be obtained at the URL http://shelah.logic.at/
At this time, the problems fully solved are: 2, 4, 10, 12, 16, 18, 20, 22, 24, 34, 35, 36, 41, 42, 46, 47, 48, 51, 52, 55, 56, 60, 62, 76, 80, 92; those partially solved are: 1, 8, 11, 13, 14, 21, 25, 26, 27, 32, 33, 37, 45, 50, 54, 73, 77, 78, 79, 81, 93; still open in the form given in [CI] are: 3, 5, 6, 7, 9, 15, 17, 19, 23, 28, 29, 30, 31, 38, 39, 40, 43, 44, 49, 53, 57, 58, 59, 61, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 82, 83, 84--91, 94-97.
Among those which are still unsolved, or partially unsolved, progress on the following may be possible without too much difficulty: 5, 7, 8, 9, 11, 13, 14, 21, 23, 29, 30, 31, 32, 33, 37, 39, 43, 44, 45, 50, 54, 64, 68, 69, 70, 71, 72, 73, 74, 77, 78, 81, 84, 86, 90, 93, 94-97.
Date published: April 26, 2000. Revised April 28, 2004