Cardinal Invariants on Boolean Algebras

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Springer Science & Business Media, Mar 25, 2010 - Mathematics - 301 pages

This text covers cardinal number valued functions defined for any Boolean algebra such as cellularity. It explores the behavior of these functions under algebraic operations such as products, free products, ultraproducts and their relationships to each other.

 

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Contents

0 Introduction
1
1 Special operations on Boolean algebras
9
2 Special classes of Boolean algebras
25
3 Cellularity
45
4 Depth
86
5 Topological density
107
6 πweight
116
7 Length
125
16 Hereditary density
196
17 Incomparability
218
18 Hereditary cofinality
226
19 Number of ultrafilters
232
20 Number of automorphisms
233
21 Number of endomorphisms
236
22 Number of ideals
238
23 Number of subalgebras
239

8 Irredundance
133
9 Cardinality
145
10 Independence
147
11 πCharacter
154
12 Tightness
164
13 Spread
175
14 Character
181
15 Hereditary Lindelof degree
190
24 Other cardinal functions
244
25 Diagrams
248
26 Examples
271
References
278
Index of problems
287
Index of symbols
293
Index of names and words
295
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