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Depth, π-character, and tightness in superatomic Boolean algebras

✍ Scribed by Alan Dow; J. Donald Monk

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
1000 KB
Volume
75
Category
Article
ISSN
0166-8641

No coin nor oath required. For personal study only.

✦ Synopsis

Theorem A. There is a superatomic Boolean algebra B with size and n-character equal to WI and countable depth. Theorem B. If B is a superatomic Boolean algebra with r-character greater than WI, then the 7r-character and depth of B are the same. Theorem C. rf rc. --f (K):~, then every superatomic Boolean algebra with tightness at least n' has depth at least K.

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Balcar, B. and P. Simon, Reaping number and n-character of Boolean algebras, Discrete Mathematics 108 (1992) 5-12. For every Boolean algebra B the minimal n-character of an ultrafilter on B is at most 2",