Set theory: Boolean-valued models and independence proofs
Gespeichert in:
| Vorheriger Titel: | Bell, John L. Boolean valued models and independence proofs in set theory |
|---|---|
| 1. Verfasser: | |
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Clarendon Press
2011
|
| Ausgabe: | 3. ed., [paperback ed.] |
| Schriftenreihe: | Oxford logic guides
47 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXII, 191 S. |
| ISBN: | 9780199609161 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804148380587261952 |
|---|---|
| adam_text | Titel: Set theory
Autor: Bell, John L
Jahr: 2011
CONTENTS
List of Problems xxi
0 Boolean and Heyting Algebras:
The Essentials 1
Lattices 1
Heyting and Boolean algebras 3
Filters, ideals, and homomorphisms 8
Representation theorems for distributive lattices 11
Connections with logic 12
1 Boolean-Valued Models of
Set Theory: First Steps 16
Basic set theory 16
Construction of the model 20
Subalgebras and their modeis 29
Mixtures and the Maximum Principle 33
The truth of the axioms of set theory in V(ß) 37
Ordinals and constructible sets in V^ 45
Cardinals in V^B 48
2 Forcing and Some Independence Proofe 55
The forcing relation 55
Independence of the aodom of constructibility and
the continuum hypothesis 60
Problems 66
3 Group Actions on V*B* and the Independence
of the Axiom of Choice 71
Group actions on V^ 71
The independence of the existence of definable
well-orderings of Po; 74
Problems 75
The independence of the axiom of choice 78
4 Generic Ultrafilters and Transitive
Models of ZFC 88
Problems 101
xx CONTENTS
5 Cardinal Collapsing, Boolean Isomorphism,
and Applications to the Theory of
Boolean Algebras 109
Cardinal collapsing 109
Boolean isomorphism and infinitary equivalence 112
Applications to the theory of Boolean algebras 116
6 Iterated Boolean Extensions, Martin s Axiom, and
Souslin s Hypothesis 120
Souslin s hypothesis 120
The independence of SH 122
Martin s axiom 125
Iterated Boolean extensions 128
Further results on Boolean algebras 137
The relative consistency of SH 142
Problems 146
7 Boolean-Valued Analysis 149
Boolean-valued modeis built from measure algebras 149
Boolean-valued modeis built from algebras of projections 153
8 Intuitionistic Set Theory and Heyting-Algebra-Valued
Models 158
Intuitionistic Zermelo set theory 158
Intuitionistic Zermelo-Fraenkel set theory 163
Heyting-algebra-valued modeis 165
Forcing in Heyting-algebra-valued modeis and
independence in IZF 167
Appendix: Boolean and Heyting Algebra-Valued Models as
Categories 169
Categories and functors 169
Toposes 175
Boolean and Heyting algebra-valued modeis as toposes 179
Historical Notes 182
Bibliography 184
Index of Symbols 188
Index 189
|
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| author | Bell, John Lane |
| author_facet | Bell, John Lane |
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| dewey-full | 511.322 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie |
| edition | 3. ed., [paperback ed.] |
| format | Book |
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| spelling | Bell, John Lane Verfasser aut Set theory Boolean-valued models and independence proofs John L. Bell 3. ed., [paperback ed.] Oxford [u.a.] Clarendon Press 2011 XXII, 191 S. txt rdacontent n rdamedia nc rdacarrier Oxford logic guides 47 Mengenlehre (DE-588)4074715-3 gnd rswk-swf Mengenlehre (DE-588)4123623-3 Lehrbuch gnd-content Mengenlehre (DE-588)4074715-3 s 1\p DE-604 Früher u.d.T. Bell, John L. Boolean valued models and independence proofs in set theory Oxford logic guides 47 (DE-604)BV000013997 47 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024409280&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bell, John Lane Set theory Boolean-valued models and independence proofs Oxford logic guides Mengenlehre (DE-588)4074715-3 gnd |
| subject_GND | (DE-588)4074715-3 (DE-588)4123623-3 |
| title | Set theory Boolean-valued models and independence proofs |
| title_auth | Set theory Boolean-valued models and independence proofs |
| title_exact_search | Set theory Boolean-valued models and independence proofs |
| title_full | Set theory Boolean-valued models and independence proofs John L. Bell |
| title_fullStr | Set theory Boolean-valued models and independence proofs John L. Bell |
| title_full_unstemmed | Set theory Boolean-valued models and independence proofs John L. Bell |
| title_old | Bell, John L. Boolean valued models and independence proofs in set theory |
| title_short | Set theory |
| title_sort | set theory boolean valued models and independence proofs |
| title_sub | Boolean-valued models and independence proofs |
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