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## Handbook of Boolean algebras / edited by J. Donald Monk, with the cooperation of Robert Bonnet.

Editor: Amsterdam : North-Holland, 1989Descripción: 3 v. (xix, 1367 p.) : il. ; 25 cmISBN: 0444872914 (set); 044470261X (v. 1); 0444871527 (v. 2); 0444871535 (v. 3)Otra clasificación: 06-02 (03B25 03C65 03D35 03G05 06Exx)
Contenidos:
```Contents of Volume 
Introduction to the Handbook v
Contents of the Handbook xi
Part I. General Theory of Boolean Algebras, by Sabine Koppelberg 
Acknowledgements 
Introduction to Part 1 
Chapter 1. Elementary arithmetic 
Introduction 
1. Examples and arithmetic of Boolean algebras 
1.1. Definitions and notation 
1.2. Algebras of sets 
1.3. Lindenbaum—Tarski algebras 
1.4. The duality principle 
1.5. Arithmetic of Boolean algebras. Connection with lattices 
1.6. Connection with Boolean rings 
1.7. Infinite operations 
1.8. Boolean algebras of projections 
1.9. Regular open algebras 
Exercises 
2. Atoms, ultrafilters, and Stone’s theorem 
2.1. Atoms 
2.2. Ultrafilters and Stone’s theorem 
2.3. Arithmetic revisited 
2.4. The Rasiowa-Sikorski lemma 
Exercises 
3. Relativization and disjointness 
3.1. Relative algebras and pairwise disjoint' families 
3.2. Attainment of cellularity: the Erdos-Tarski theorem 
3.3. Disjoint refinements: the Balcar-Vojtas theorem 
Exercises 
Chapter 2. Algebraic theory 
Introduction 
4. Subalgebras, denseness, and incomparability 
4.1. Normal forms 
4.2. The completion of a partial order 
4.3. The completion of a Boolean algebra 
4.4. Irredundance and pairwise incomparable families 
Exercises 
5. Homomorphisms, ideals, and quotients 
5.1. Homomorphic extensions 
5.2. Sikorski's extension theorem 
5.3. Vaught's isomorphism theorem 
5.4. Ideals and quotients 
5.5. The algebra P(w)/fin 
5.6. The number of ultrafilters, filters, and subalgebras 
Exercises 
6. Products 
6.1. Product decompositions and partitions 
6.2. Hanfs example 
Exercises 
Chapter 3. Topological duality 
Introduction 
7. Boolean algebras and Boolean spaces 
7.1. Boolean spaces 
7.2. The topological version of Stone’s theorem 
7.3. Dual properties of A and Ult A 
Exercises 
8. Homomorphisms and continuous maps 
8.1. Duality of homomorphisms and continuous maps 
8.2. Subalgebras and Boolean equivalence relations 
8.3. Product algebras and compactifications 
8.4. The sheaf representation of a Boolean algebra over a subalgebra 
Exercises 
Chapter 4. Free constructions 
Introduction 
9. Free Boolean algebras 
9.1. General facts 
9.2. Algebraic and combinatorial properties of free algebras 
Exercises 
10, Independence and the number of ideals 
10.1. Independence and chain conditions 
10.2. The number of ideals of a Boolean algebra 
10.3. A characterization of independence 
Exercises 
11. Free products 
11.1. Free products 
11.2. Homogeneity, chain conditions, and independence in free products 
11.3. Amalgamated free products 
Exercises 
Chapter 5. Infinite operations 
Introduction 
12. k-complete algebras 
12.1. The countable separation property 
12.2. A Schroder-Bernstein theorem 
12.3. The Loomis-Sikorski theorem 
12.4. Amalgamated free products and injectivity in the category of
x-complete Boolean algebras 
Exercises 
13. Complete algebras 
13.1. Countably generated complete algebras 
13.2. The Balcar-Franek theorem 
13.3. Two applications of the Balcar-Franek theorem 
13.4. Automorphisms of complete algebras: Frolik’s theorem 
Exercises 
14. Distributive laws 
14.1. Definitions and examples 
14.2. Equivalences to distributivity 
14.3. Distributivity and representability 
14.4. Three-parameter distributivity 
14.5. Distributive laws in regular open algebras of trees 
14.6. Weak distributivity 
Exercises 
Chapter 6. Special classes of Boolean algebras 
Introduction 
15. Interval algebras 
15.1. Characterization of interval algebras and their dual spaces 
15.2. Closure properties of interval algebras 
15.3. Retractive algebras 
15.4. Chains and antichains in subalgebras of interval algebras 
Exercises 
16. Tree algebras 
16.1. Normal forms 
16.2. Basic facts on tree algebras 
16.3. A construction of rigid Boolean algebras 
16.4. Closure properties of tree algebras 
Exercises 
17. Superatomic algebras 
17.1. Characterizations of superatomicity 
17.2. The Cantor-Bendixson invariants 
17.3. Cardinal sequences 
Exercises 
Chapter 7. Metamathematics 
Introduction 
18. Decidability of the first order theory of Boolean algebras 
18.1. The elementary invariants 
18.2. Elementary equivalence of Boolean algebras 
18.3. The decidability proof 
Exercises 
19. Undecidability of the first order theory of Boolean algebras with a distinguished subalgebra 
19.1. The method of semantical embeddings 
19.2. Undecidability of Th (BP*) 
Exercises 
References to Part I 
Index of notation, Volume 1 312a
Index, Volume 1 312f```
```Contents of Volume 
Introduction to the Handbook v
Contents of the Handbook xi
Part II. Topics in the theory of Boolean algebras 
Section A. Arithmetical properties of Boolean algebras 
Chapter 8. Distributive laws, by Thomas Jech 
References 
Chapter 9. Disjoint refinement, by Bohuslav Balcar and Petr Simon 
0. Introduction 
1. The disjoint refinement property in Boolean algebras 
2. The disjoint refinement property of centred systems in Boolean algebras 
3. Non-distributivity of P(w) /fin 
4. Refinements by countable sets 
5. The algebra P(k)/[k]<k; non-distributivity and decomposability 
References 
Section B. Algebraic properties of Boolean algebras 
Chapter 10. Subalgebras, by Robert Bonnet 
0. Introduction 
1. Characterization of the lattice of subalgebras of a Boolean algebra 
2. Complementation and retractiveness in Sub(B) 
3. Quasi-complements 
4. Congruences on the lattice of subalgebras 
References 
Chapter 11. Cardinal functions on Boolean spaces, by Eric K, van Douwen 
1. Introduction 
2. Conventions 
3. A little bit of topology 
4. New cardinal functions from old 
5. Topological cardinal functions: c, d, L, t, w, π, Xc, πx 
6. Basic results 
7. Variations of independence 
II 8. π-weight and π-character 
9. Character and cardinality, independence and π-character 
10. Getting small dense subsets by killing witnesses 
11. Weakly countably complete algebras 
12. Cofinality of Boolean algebras and some other small cardinal functions 
13. Survey of results 
14. The free BA on k generators 
References and mathematicians mentioned 
Chapter 12. The number of Boolean algebras, by J. Donald Monk 
0. Introduction 
1. Simple constructions 
2. Construction of complicated Boolean algebras 
References 
Chapter 13. Endomorphisms of Boolean algebras, by J. Donald Monk 
0. Introduction 
1. Reconstruction 
2. Number of endomorphisms 
3. Endo-rigid algebras 
4. Hopfian Boolean algebras 
Problems 
References 
Chapter 14. Automorphism groups, by J. Donald Monk 
0. Introduction 
1. General properties 
2. Galois theory of simple extensions 
3. Galois theory of finite extensions 
4. The size of automorphism groups 
References 
Chapter 15. On the reconstruction of Boolean algebras from their automorphism groups, by Matatyahu Rubin 
1. Introduction 
2. The method 
3. Faithfulness in the class of complete Boolean algebras 
4. Faithfulness of incomplete Boolean algebras 
5. Countable Boolean algebras 
6. Faithfulness of measure algebras 
References 
Chapter 16. Embeddings and automorphisms, by Petr Stepánek 
0. Introduction 
1. Rigid complete Boolean algebras 
2. Embeddings into complete rigid algebras 
3. Embeddings into the center of a Boolean algebra 
4. Boolean algebras with no rigid or homogeneous factors 
5. Embeddings into algebras with a trivial center 
References 
Chapter 17. Rigid Boolean algebras, by Mohamed Bekkali and Robert Bonnet 
0. Introduction 
1. Basic concepts concerning orderings and trees 
2. The Jonsson construction of a rigid algebra 
3. Bonnet’s construction of mono-rigid interval algebras 
4. Todorcevic’s construction of many mono-rigid interval algebras 
5. Jech’s construction of simple complete algebras 
6. Odds and ends on rigid algebras 
References 
Chapter 18. Homogeneous Boolean algebras, by Petr Stepanek and Matatyahu Rubin 
0. Introduction 
1. Homogeneous algebras 
2. Weakly homogeneous algebras 
3. k -universal homogeneous algebras 
4. Complete weakly homogeneous algebras 
5. Results and problems concerning the simplicity of automorphism groups of homogeneous BAs 
6. Stronger forms of homogeneity 
References 
Index of notation, Volume 2 716a
Index, Volume 2 716j```
```Contents of Volume 
Introduction to the Handbook
Contents of the Handbook xi
Part II. Topics in the theory of Boolean algebras (continued) 
Section C. Special classes of Boolean algebras 
Chapter 19. Superatomic Boolean algebras, by Judy Roitman 
Introduction 
Preliminaries 
Odds and ends 
Thin-tall Boolean algebras 
No big sBAs 
More negative results 
A very thin thick sBA 
Any countable group can be G(B) 
References 
Chapter 20. Projective Boolean algebras, by Sabine Koppefberg 
Introduction 
Elementary results 
Characterizations of projective algebras 
Characters of ultrafilters 
The number of projective Boolean algebras 
References 
Chapter 21. Countable Boolean algebras, by R.S. Pierce 
Introduction 
Invariants 
Algebras of isomorphism types 
Special classes of algebras 
References 
Chapter 22. Measure algebras, by David H. Fremlin 
Introduction 
Measure theory 
Measure algebras 
Maharam’s theorem 
Liftings 
Which algebras are measurable? 
Cardinal functions 
Envoi: Atomlessly-measurable cardinals 
References 
Section D. Logical questions 
Chapter 23. Decidable extensions of the theory of Boolean algebras, by
Martin Weese 
Introduction 
Describing the languages 
The monadic theory of countable linear orders and its application to the theory of Boolean algebras 
The theories Thu(BA) and ThQd(BA) 
Ramsey quantifiers and sequence quantifiers 
The theory of Boolean algebras with cardinality quantifiers 
Residually small discriminator varieties 
Boolean algebras with a distinguished finite automorphism group 
Boolean pairs 
References 
Chapter 24. Undecidable extensions of the theory of Boolean algebras, by Martin Weese 
Introduction 
Boolean algebras in weak second-order logic and second-order logic 
Boolean algebras in a logic with the Härtig quantifier 
Boolean algebras in a logic with the Malitz quantifier 
Boolean algebras in stationary logic 
Boolean algebras with a distinguished group of automorphisms 
Single Boolean algebras with a distinguished ideal 
Boolean algebras in a logic with quantification over ideals 
Some applications 
References 
Chapter 25. Recursive Boolean algebras, by J.B. Remmel 
Introduction 
Preliminaries 
Equivalent characterizations of recursive, r.e., and arithmetic BAs 
Recursive Boolean algebras with highly effective presentations 
Recursive Boolean algebras with minimally effective presentations 
Recursive isomorphism types of Rec. BAs 
The lattices of r.e. subalgebras and r.e. ideals of a Rec. BA 
Recursive automorphisms of Rec. BAs 
References 
Chapter 26. Lindenbaum-Tarski algebras, by Dale Myers 
Introduction 
History 
Sentence algebras and model spaces 
Model maps 
Duality 
Repetition and Cantor-Bernstein 
Language isomorphisms 
Measures 
Rank diagrams 
Interval algebras and cut spaces 
Factor measures 
Measure monoids 
Orbits 
Primitive spaces and orbit diagrams 
Miscellaneous 
Table of sentence algebras 
References 
Chapter 27. Boolean-valued models, by Thomas Jech 
Appendix on set theory, by J. Donald Monk 
Introduction 
Cardinal arithmetic 
Two lemmas on the unit interval 
Almost-disjoint sets 
Independent sets 
Stationary sets 
∆-systems 
The partition calculus 
Hajnal’s free set theorem 
References 
Chart of topological duality 
Appendix on general topology, by Bohuslav Balcar and Petr Simon 
Introduction 
Basics 
Separation axioms 
Compactness 
The Cech-Stone compactification 
Extremally disconnected and Gleason spaces 
K-Parovicenko spaces 
F-spaces 
Cardinal invariants 
References 
Bibliography 
General 
Elementary 
Functional analysis 
Logic 
Measure algebras 
Recursive BAs 
Set theory and BAs 
Topology and BAs 
Topological BAs 
Index of notation, Volume 3 
Index, Volume 3 ``` Average rating: 0.0 (0 votes)
Item type Home library Call number Materials specified Status Date due Barcode Course reserves Libros
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06 H236 (Browse shelf) Vol. 3 Available A-6360

Vol. 1 por Sabine Koppelberg.

Incluye referencias bibliográficas e índices.

Contents of Volume  --
Introduction to the Handbook v --
Contents of the Handbook xi --
Part I. General Theory of Boolean Algebras, by Sabine Koppelberg  --
Acknowledgements  --
Introduction to Part 1  --
Chapter 1. Elementary arithmetic  --
Introduction  --
1. Examples and arithmetic of Boolean algebras  --
1.1. Definitions and notation  --
1.2. Algebras of sets  --
1.3. Lindenbaum—Tarski algebras  --
1.4. The duality principle  --
1.5. Arithmetic of Boolean algebras. Connection with lattices  --
1.6. Connection with Boolean rings  --
1.7. Infinite operations  --
1.8. Boolean algebras of projections  --
1.9. Regular open algebras  --
Exercises  --
2. Atoms, ultrafilters, and Stone’s theorem  --
2.1. Atoms  --
2.2. Ultrafilters and Stone’s theorem  --
2.3. Arithmetic revisited  --
2.4. The Rasiowa-Sikorski lemma  --
Exercises  --
3. Relativization and disjointness  --
3.1. Relative algebras and pairwise disjoint' families  --
3.2. Attainment of cellularity: the Erdos-Tarski theorem  --
3.3. Disjoint refinements: the Balcar-Vojtas theorem  --
Exercises  --
Chapter 2. Algebraic theory  --
Introduction  --
4. Subalgebras, denseness, and incomparability  --
4.1. Normal forms  --
4.2. The completion of a partial order  --
4.3. The completion of a Boolean algebra  --
4.4. Irredundance and pairwise incomparable families  --
Exercises  --
5. Homomorphisms, ideals, and quotients  --
5.1. Homomorphic extensions  --
5.2. Sikorski's extension theorem  --
5.3. Vaught's isomorphism theorem  --
5.4. Ideals and quotients  --
5.5. The algebra P(w)/fin  --
5.6. The number of ultrafilters, filters, and subalgebras  --
Exercises  --
6. Products  --
6.1. Product decompositions and partitions  --
6.2. Hanfs example  --
Exercises  --
Chapter 3. Topological duality  --
Introduction  --
7. Boolean algebras and Boolean spaces  --
7.1. Boolean spaces  --
7.2. The topological version of Stone’s theorem  --
7.3. Dual properties of A and Ult A  --
Exercises  --
8. Homomorphisms and continuous maps  --
8.1. Duality of homomorphisms and continuous maps  --
8.2. Subalgebras and Boolean equivalence relations  --
8.3. Product algebras and compactifications  --
8.4. The sheaf representation of a Boolean algebra over a subalgebra  --
Exercises  --
Chapter 4. Free constructions  --
Introduction  --
9. Free Boolean algebras  --
9.1. General facts  --
9.2. Algebraic and combinatorial properties of free algebras  --
Exercises  --
10, Independence and the number of ideals  --
10.1. Independence and chain conditions  --
10.2. The number of ideals of a Boolean algebra  --
10.3. A characterization of independence  --
Exercises  --
11. Free products  --
11.1. Free products  --
11.2. Homogeneity, chain conditions, and independence in free products  --
11.3. Amalgamated free products  --
Exercises  --
Chapter 5. Infinite operations  --
Introduction  --
12. k-complete algebras  --
12.1. The countable separation property  --
12.2. A Schroder-Bernstein theorem  --
12.3. The Loomis-Sikorski theorem  --
12.4. Amalgamated free products and injectivity in the category of --
x-complete Boolean algebras  --
Exercises  --
13. Complete algebras  --
13.1. Countably generated complete algebras  --
13.2. The Balcar-Franek theorem  --
13.3. Two applications of the Balcar-Franek theorem  --
13.4. Automorphisms of complete algebras: Frolik’s theorem  --
Exercises  --
14. Distributive laws  --
14.1. Definitions and examples  --
14.2. Equivalences to distributivity  --
14.3. Distributivity and representability  --
14.4. Three-parameter distributivity  --
14.5. Distributive laws in regular open algebras of trees  --
14.6. Weak distributivity  --
Exercises  --
Chapter 6. Special classes of Boolean algebras  --
Introduction  --
15. Interval algebras  --
15.1. Characterization of interval algebras and their dual spaces  --
15.2. Closure properties of interval algebras  --
15.3. Retractive algebras  --
15.4. Chains and antichains in subalgebras of interval algebras  --
Exercises  --
16. Tree algebras  --
16.1. Normal forms  --
16.2. Basic facts on tree algebras  --
16.3. A construction of rigid Boolean algebras  --
16.4. Closure properties of tree algebras  --
Exercises  --
17. Superatomic algebras  --
17.1. Characterizations of superatomicity  --
17.2. The Cantor-Bendixson invariants  --
17.3. Cardinal sequences  --
Exercises  --
Chapter 7. Metamathematics  --
Introduction  --
18. Decidability of the first order theory of Boolean algebras  --
18.1. The elementary invariants  --
18.2. Elementary equivalence of Boolean algebras  --
18.3. The decidability proof  --
Exercises  --
19. Undecidability of the first order theory of Boolean algebras with a distinguished subalgebra  --
19.1. The method of semantical embeddings  --
19.2. Undecidability of Th (BP*)  --
Exercises  --
References to Part I  --
Index of notation, Volume 1 312a --
Index, Volume 1 312f --

Contents of Volume  --
Introduction to the Handbook v --
Contents of the Handbook xi --
Part II. Topics in the theory of Boolean algebras  --
Section A. Arithmetical properties of Boolean algebras  --
Chapter 8. Distributive laws, by Thomas Jech  --
References  --
Chapter 9. Disjoint refinement, by Bohuslav Balcar and Petr Simon  --
0. Introduction  --
1. The disjoint refinement property in Boolean algebras  --
2. The disjoint refinement property of centred systems in Boolean algebras  --
3. Non-distributivity of P(w) /fin  --
4. Refinements by countable sets  --
5. The algebra P(k)/[k]<k; non-distributivity and decomposability  --
References  --
Section B. Algebraic properties of Boolean algebras  --
Chapter 10. Subalgebras, by Robert Bonnet  --
0. Introduction  --
1. Characterization of the lattice of subalgebras of a Boolean algebra  --
2. Complementation and retractiveness in Sub(B)  --
3. Quasi-complements  --
4. Congruences on the lattice of subalgebras  --
References  --
Chapter 11. Cardinal functions on Boolean spaces, by Eric K, van Douwen  --
1. Introduction  --
2. Conventions  --
3. A little bit of topology  --
4. New cardinal functions from old  --
5. Topological cardinal functions: c, d, L, t, w, π, Xc, πx  --
6. Basic results  --
7. Variations of independence  --
II 8. π-weight and π-character  --
9. Character and cardinality, independence and π-character  --
10. Getting small dense subsets by killing witnesses  --
11. Weakly countably complete algebras  --
12. Cofinality of Boolean algebras and some other small cardinal functions  --
13. Survey of results  --
14. The free BA on k generators  --
References and mathematicians mentioned  --
Chapter 12. The number of Boolean algebras, by J. Donald Monk  --
0. Introduction  --
1. Simple constructions  --
2. Construction of complicated Boolean algebras  --
References  --
Chapter 13. Endomorphisms of Boolean algebras, by J. Donald Monk  --
0. Introduction  --
1. Reconstruction  --
2. Number of endomorphisms  --
3. Endo-rigid algebras  --
4. Hopfian Boolean algebras  --
Problems  --
References  --
Chapter 14. Automorphism groups, by J. Donald Monk  --
0. Introduction  --
1. General properties  --
2. Galois theory of simple extensions  --
3. Galois theory of finite extensions  --
4. The size of automorphism groups  --
References  --
Chapter 15. On the reconstruction of Boolean algebras from their automorphism groups, by Matatyahu Rubin  --
1. Introduction  --
2. The method  --
3. Faithfulness in the class of complete Boolean algebras  --
4. Faithfulness of incomplete Boolean algebras  --
5. Countable Boolean algebras  --
6. Faithfulness of measure algebras  --
References  --
Chapter 16. Embeddings and automorphisms, by Petr Stepánek  --
0. Introduction  --
1. Rigid complete Boolean algebras  --
2. Embeddings into complete rigid algebras  --
3. Embeddings into the center of a Boolean algebra  --
4. Boolean algebras with no rigid or homogeneous factors  --
5. Embeddings into algebras with a trivial center  --
References  --
Chapter 17. Rigid Boolean algebras, by Mohamed Bekkali and Robert Bonnet  --
0. Introduction  --
1. Basic concepts concerning orderings and trees  --
2. The Jonsson construction of a rigid algebra  --
3. Bonnet’s construction of mono-rigid interval algebras  --
4. Todorcevic’s construction of many mono-rigid interval algebras  --
5. Jech’s construction of simple complete algebras  --
6. Odds and ends on rigid algebras  --
References  --
Chapter 18. Homogeneous Boolean algebras, by Petr Stepanek and Matatyahu Rubin  --
0. Introduction  --
1. Homogeneous algebras  --
2. Weakly homogeneous algebras  --
3. k -universal homogeneous algebras  --
4. Complete weakly homogeneous algebras  --
5. Results and problems concerning the simplicity of automorphism groups of homogeneous BAs  --
6. Stronger forms of homogeneity  --
References  --
Index of notation, Volume 2 716a --
Index, Volume 2 716j --

Contents of Volume  --
Introduction to the Handbook --
Contents of the Handbook xi --
Part II. Topics in the theory of Boolean algebras (continued)  --
Section C. Special classes of Boolean algebras  --
Chapter 19. Superatomic Boolean algebras, by Judy Roitman  --
Introduction  --
Preliminaries  --
Odds and ends  --
Thin-tall Boolean algebras  --
No big sBAs  --
More negative results  --
A very thin thick sBA  --
Any countable group can be G(B)  --
References  --
Chapter 20. Projective Boolean algebras, by Sabine Koppefberg  --
Introduction  --
Elementary results  --
Characterizations of projective algebras  --
Characters of ultrafilters  --
The number of projective Boolean algebras  --
References  --
Chapter 21. Countable Boolean algebras, by R.S. Pierce  --
Introduction  --
Invariants  --
Algebras of isomorphism types  --
Special classes of algebras  --
References  --
Chapter 22. Measure algebras, by David H. Fremlin  --
Introduction  --
Measure theory  --
Measure algebras  --
Maharam’s theorem  --
Liftings  --
Which algebras are measurable?  --
Cardinal functions  --
Envoi: Atomlessly-measurable cardinals  --
References  --
Section D. Logical questions  --
Chapter 23. Decidable extensions of the theory of Boolean algebras, by --
Martin Weese  --
Introduction  --
Describing the languages  --
The monadic theory of countable linear orders and its application to the theory of Boolean algebras  --
The theories Thu(BA) and ThQd(BA)  --
Ramsey quantifiers and sequence quantifiers  --
The theory of Boolean algebras with cardinality quantifiers  --
Residually small discriminator varieties  --
Boolean algebras with a distinguished finite automorphism group  --
Boolean pairs  --
References  --
Chapter 24. Undecidable extensions of the theory of Boolean algebras, by Martin Weese  --
Introduction  --
Boolean algebras in weak second-order logic and second-order logic  --
Boolean algebras in a logic with the Härtig quantifier  --
Boolean algebras in a logic with the Malitz quantifier  --
Boolean algebras in stationary logic  --
Boolean algebras with a distinguished group of automorphisms  --
Single Boolean algebras with a distinguished ideal  --
Boolean algebras in a logic with quantification over ideals  --
Some applications  --
References  --
Chapter 25. Recursive Boolean algebras, by J.B. Remmel  --
Introduction  --
Preliminaries  --
Equivalent characterizations of recursive, r.e., and arithmetic BAs  --
Recursive Boolean algebras with highly effective presentations  --
Recursive Boolean algebras with minimally effective presentations  --
Recursive isomorphism types of Rec. BAs  --
The lattices of r.e. subalgebras and r.e. ideals of a Rec. BA  --
Recursive automorphisms of Rec. BAs  --
References  --
Chapter 26. Lindenbaum-Tarski algebras, by Dale Myers  --
Introduction  --
History  --
Sentence algebras and model spaces  --
Model maps  --
Duality  --
Repetition and Cantor-Bernstein  --
Language isomorphisms  --
Measures  --
Rank diagrams  --
Interval algebras and cut spaces  --
Factor measures  --
Measure monoids  --
Orbits  --
Primitive spaces and orbit diagrams  --
Miscellaneous  --
Table of sentence algebras  --
References  --
Chapter 27. Boolean-valued models, by Thomas Jech  --
Appendix on set theory, by J. Donald Monk  --
Introduction  --
Cardinal arithmetic  --
Two lemmas on the unit interval  --
Almost-disjoint sets  --
Independent sets  --
Stationary sets  --
∆-systems  --
The partition calculus  --
Hajnal’s free set theorem  --
References  --
Chart of topological duality  --
Appendix on general topology, by Bohuslav Balcar and Petr Simon  --
Introduction  --
Basics  --
Separation axioms  --
Compactness  --
The Cech-Stone compactification  --
Extremally disconnected and Gleason spaces  --
K-Parovicenko spaces  --
F-spaces  --
Cardinal invariants  --
References  --
Bibliography  --
General  --
Elementary  --
Functional analysis  --
Logic  --
Measure algebras  --
Recursive BAs  --
Set theory and BAs  --
Topology and BAs  --
Topological BAs  --
Index of notation, Volume 3  --
Index, Volume 3  --

MR, 90k:06002 (v. 1)

MR, 90k:06003 (v. 2)

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