Cardinal Invariants on Boolean AlgebrasThis 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. |
Contents
| 1 | |
| 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 |
| 293 | |
| 295 | |
Other editions - View all
Common terms and phrases
assume atoms attained AutA Boolean algebras cardinal cellularity Chapter choose claim clear Clearly clopen closed compact complete consider consistent construct contradiction Corollary countable define definition dense Depth desired dIef difference disjoint distinct easy elements equivalent example exist extension fact finite first free sequence function give given Handbook hence holds homomorphic image ideal implies independent infinite BA infinite cardinal interval algebra IrrA isomorphic least Lemma length limit Monk 90 Note obvious otherwise possible Problem Proof Proposition prove regular relation result sense sequence Shelah space strictly increasing subalgebra subset successor superatomic suppose Theorem topology tree algebra UltA ultrafilter uncountable