This is a greatly revised and expanded version of the book Cardinal
fu- tionsonBooleanalgebras, Birkh]
auser1990.Knownmistakesinthatbookhave beencorrected,
andmanyoftheproblemsstatedtherehavesolutionsinthepresent treatment.
At the same time, many new problems are formulated here; some as
development of the solved problems from the earlier work, but most
as a result of more careful study of the notions. The book is
supposed to be self-contained, and for that reason many classical
results are included. ForhelponthisbookIwishtothankE.K.vanDouwen,
K.Grant, L. Heindorf, I. Juh asz, S. Koppelberg, P. Koszmider, P.
Nyikos, D. Peterson, M. Rubin, S. Shelah, and S. Todor? cevi c.
Unpublished results of some of these people are contained here,
sometimes with proofs, with their permission. As the reader will
see, my greatest debt is to Saharon Shelah, who has worked on, and
solved, many of the problems stated in the 1990 book as well as in
preliminary versions of this book. Of course I am always eager to
hear about solutions of problems, mistakes, etc. Electronic lists
of errata and the status of the open problems are maintained,
initially on the anonymous ftp server of euclid.colorado.edu,
directory pub/babib; on www, go to ftp:
//euclid.colorado.edu/pub/babib."
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