Set theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2006
|
| Ausgabe: | 3. millenium ed., rev. and expanded; corr. 4. print. |
| Schriftenreihe: | Springer monographs in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 769 S. |
| ISBN: | 3540440852 9783540440857 |
Internformat
MARC
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| 245 | 1 | 0 | |a Set theory |c Thomas Jech |
| 250 | |a 3. millenium ed., rev. and expanded; corr. 4. print. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2006 | |
| 300 | |a XIII, 769 S. | ||
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Datensatz im Suchindex
| _version_ | 1804136644613242880 |
|---|---|
| adam_text | Table
Part
1.
Axioms of Zermelo-Fraenkel. Why Axiomatic Set Theory? Language of Set
Theory, Formulas. Classes. Extensionality. Pairing. Separation Schema.
Union. Power Set. Infinity. Replacement Schema. Exercises. Historical Notes.
2.
Linear and Partial Ordering. Well-Ordering. Ordinal Numbers. Induction and
Recursion. Ordinal Arithmetic. Well-Founded Relations. Exercises. Historical
Notes.
3.
Cardinality. Alephs. The Canonical Well-Ordering of
ercises. Historical Notes.
4.
The Cardinality of the Continuum. The Ordering of R. Suslin s Problem. The
Topology of the Real Line.
Polish Spaces. Exercises. Historical Notes.
5.
The Axiom of Choice. Using the Axiom of Choice in Mathematics. The Count¬
able Axiom of Choice. Cardinal Arithmetic. Infinite Sums and Products. The
Continuum Function. Cardinal Exponentiation. The Singular Cardinal Hy¬
pothesis. Exercises. Historical Notes.
6.
The Cumulative Hierarchy of Sets.
Bernays-Gödel
7.
Filters and
Boolean Algebras. Ideals and Filters on Boolean Algebras. Complete Boolean
Algebras. Complete and Regular Subalgebras. Saturation. Distributivity of
Complete Boolean Algebras. Exercises. Historical Notes.
X Table of Contents
8.
Closed Unbounded Sets. Mahlo Cardinals. Normal Filters. Silver s Theo¬
rem. A Hierarchy of Stationary Sets. The Closed Unbounded Filter on
Exercises. Historical Notes.
9.
Partition Properties. Weakly Compact Cardinals. Trees. Almost Disjoint Sets
and Functions. The Tree Property and Weakly Compact Cardinals. Ramsey
Cardinals. Exercises. Historical Notes.
10.
The Measure Problem. Measurable and Real-Valued Measurable Cardinals.
Measurable Cardinals. Normal Measures. Strongly Compact and Supercom-
pact Cardinals. Exercises. Historical Notes.
11.
Borei
Sets. Lebesgue Measure. The Property of Baire. Analytic Sets: Measure,
Category, and the Perfect Set Property. Exercises. Historical Notes.
12.
Review of Model Theory.
duced Products and Ultraproducts. Models of Set Theory and Relativization.
Relative Consistency. Transitive Models and
the Axiom of Regularity. Inaccessibility of Inaccessible Cardinals. Reflection
Principle. Exercises. Historical Notes.
Part II. Advanced Set Theory
13.
The Hierarchy of Constructible Sets.
The Levy Hierarchy. Absoluteness of Constructibility. Consistency of the Ax¬
iom of Choice. Consistency of the Generalized Continuum Hypothesis. Relative
Constructibility. Ordinal-Definable Sets. More on Inner Models. Exercises.
Historical Notes.
14.
Forcing Conditions and Generic Sets. Separative Quotients and Complete
Boolean Algebras. Boolean-Valued Models. The Boolean-Valued Model VB
The Forcing Relation. The Forcing Theorem and the Generic Model Theorem.
Consistency Proofs. Independence of the Continuum Hypothesis. Indepen¬
dence of the Axiom of Choice. Exercises. Historical Notes.
15.
Cohen Reals. Adding Subsets of Regular Cardinals. The
Distributivity. Product Forcing. Easton s Theorem. Forcing with a Class of
Conditions. The Levy Collapse. Suslin Trees. Random Reals. Forcing with
Perfect Trees. More on Generic Extensions. Symmetric Submodels of Generic
Models. Exercises. Historical Notes.
Table
16.
Two-Step Iteration. Iteration with Finite Support. Martin s Axiom. Indepen¬
dence of Suslin s Hypothesis. More Applications of Martin s Axiom. Iterated
Forcing. Exercises. Historical Notes.
17.
Ultrapowers
ity Partitions and Models. Exercises. Historical Notes.
18.
Silver
and 08. Elementary Embeddings of L. Jensen s Covering Theorem. Exercises.
Historical Notes.
19.
The Model
ers. Uniqueness of the Model L[D .
The Mitchell Order. The Models L[U]. Exercises. Historical Notes.
20.
Strongly Compact Cardinals.
pactness. Extenders and Strong Cardinals. Exercises. Historical Notes.
21.
Mild Extensions. Kunen-Paris Forcing. Silver s Forcing.
surability of Ki in ZF. Exercises. Historical Notes.
22.
Real-Valued Measurable Cardinals. Generic
Saturated Ideals. Consistency Strength of Precipitousness. Exercises. Histor¬
ical Notes.
23.
Some Combinatorial Principles. Stationary Sets in Generic Extensions. Pre¬
cipitousness of the Nonstationary Ideal. Saturation of the Nonstationary Ideal.
Reflection. Exercises. Historical Notes.
24.
The Galvin-Hajnal Theorem. Ordinal Functions and Scales. The pcf Theory.
The Structure of pcf. Transitive Generators and Localization. Shelah s Bound
on
25.
The Hierarchy of
and
Uniformization.
Codes. Exercises. Historical Notes.
XII Table of
26.
Random and Cohen reals. Solovay Sets of Reals. The Levy Collapse. Solo-
vay s Theorem. Lebesgue Measurability of
Mathias
Part III. Selected Topics
27.
The Fine Structure Theory. The Principle Ds. The Jensen Hierarchy.
Standard Codes and Standard Parameters. Diamond Principles. Trees in L.
Canonical Functions on
28.
A Nonconstructible
Tree. Consistency of Borel s Conjecture. K+-Aronszajn Trees. Exercises. His¬
torical Notes.
29.
Ramsey Theory. Gaps in
Subsets of
30.
Measure Algebras. Cohen Algebras. Suslin Algebras. Simple Algebras. Infinite
Games on Boolean Algebras. Exercises. Historical Notes.
31.
Definition and Examples. Iteration of Proper Forcing. The Proper Forcing
Axiom. Applications of PFA. Exercises. Historical Notes.
32.
Tl Equivalence Relations.
and Perfect Sets.
Exercises. Historical Notes.
33.
Determinacy and Choice. Some Consequences of AD. AD and Large Cardinals.
Projective
34.
Woodin Cardinals.
Forcing. Weakly Homogeneous Trees. Exercises. Historical Notes.
35.
The Core Model. The Covering Theorem for K. The Covering Theorem
for L[U]. The Core Model for Sequences of Measures. Up to a Strong Cardinal.
Inner Models for Woodin Cardinals. Exercises. Historical Notes.
Table
36.
Violating GCH at a Measurable Cardinal. The Singular Cardinal Problem.
Violating
Historical Notes.
37.
RCS iteration of
Reflection Principles. Forcing Axioms. Exercises. Historical Notes.
38.
The Nonstationary Ideal on Mi. Saturation and Precipitousness. Reflection.
Stationary Sets in
Historical Notes.
Bibliography
Notation
Name Index
Index
|
| adam_txt |
Table
Part
1.
Axioms of Zermelo-Fraenkel. Why Axiomatic Set Theory? Language of Set
Theory, Formulas. Classes. Extensionality. Pairing. Separation Schema.
Union. Power Set. Infinity. Replacement Schema. Exercises. Historical Notes.
2.
Linear and Partial Ordering. Well-Ordering. Ordinal Numbers. Induction and
Recursion. Ordinal Arithmetic. Well-Founded Relations. Exercises. Historical
Notes.
3.
Cardinality. Alephs. The Canonical Well-Ordering of
ercises. Historical Notes.
4.
The Cardinality of the Continuum. The Ordering of R. Suslin's Problem. The
Topology of the Real Line.
Polish Spaces. Exercises. Historical Notes.
5.
The Axiom of Choice. Using the Axiom of Choice in Mathematics. The Count¬
able Axiom of Choice. Cardinal Arithmetic. Infinite Sums and Products. The
Continuum Function. Cardinal Exponentiation. The Singular Cardinal Hy¬
pothesis. Exercises. Historical Notes.
6.
The Cumulative Hierarchy of Sets.
Bernays-Gödel
7.
Filters and
Boolean Algebras. Ideals and Filters on Boolean Algebras. Complete Boolean
Algebras. Complete and Regular Subalgebras. Saturation. Distributivity of
Complete Boolean Algebras. Exercises. Historical Notes.
X Table of Contents
8.
Closed Unbounded Sets. Mahlo Cardinals. Normal Filters. Silver's Theo¬
rem. A Hierarchy of Stationary Sets. The Closed Unbounded Filter on
Exercises. Historical Notes.
9.
Partition Properties. Weakly Compact Cardinals. Trees. Almost Disjoint Sets
and Functions. The Tree Property and Weakly Compact Cardinals. Ramsey
Cardinals. Exercises. Historical Notes.
10.
The Measure Problem. Measurable and Real-Valued Measurable Cardinals.
Measurable Cardinals. Normal Measures. Strongly Compact and Supercom-
pact Cardinals. Exercises. Historical Notes.
11.
Borei
Sets. Lebesgue Measure. The Property of Baire. Analytic Sets: Measure,
Category, and the Perfect Set Property. Exercises. Historical Notes.
12.
Review of Model Theory.
duced Products and Ultraproducts. Models of Set Theory and Relativization.
Relative Consistency. Transitive Models and
the Axiom of Regularity. Inaccessibility of Inaccessible Cardinals. Reflection
Principle. Exercises. Historical Notes.
Part II. Advanced Set Theory
13.
The Hierarchy of Constructible Sets.
The Levy Hierarchy. Absoluteness of Constructibility. Consistency of the Ax¬
iom of Choice. Consistency of the Generalized Continuum Hypothesis. Relative
Constructibility. Ordinal-Definable Sets. More on Inner Models. Exercises.
Historical Notes.
14.
Forcing Conditions and Generic Sets. Separative Quotients and Complete
Boolean Algebras. Boolean-Valued Models. The Boolean-Valued Model VB
The Forcing Relation. The Forcing Theorem and the Generic Model Theorem.
Consistency Proofs. Independence of the Continuum Hypothesis. Indepen¬
dence of the Axiom of Choice. Exercises. Historical Notes.
15.
Cohen Reals. Adding Subsets of Regular Cardinals. The
Distributivity. Product Forcing. Easton's Theorem. Forcing with a Class of
Conditions. The Levy Collapse. Suslin Trees. Random Reals. Forcing with
Perfect Trees. More on Generic Extensions. Symmetric Submodels of Generic
Models. Exercises. Historical Notes.
Table
16.
Two-Step Iteration. Iteration with Finite Support. Martin's Axiom. Indepen¬
dence of Suslin's Hypothesis. More Applications of Martin's Axiom. Iterated
Forcing. Exercises. Historical Notes.
17.
Ultrapowers
ity Partitions and Models. Exercises. Historical Notes.
18.
Silver
and 08. Elementary Embeddings of L. Jensen's Covering Theorem. Exercises.
Historical Notes.
19.
The Model
ers. Uniqueness of the Model L[D\.
The Mitchell Order. The Models L[U]. Exercises. Historical Notes.
20.
Strongly Compact Cardinals.
pactness. Extenders and Strong Cardinals. Exercises. Historical Notes.
21.
Mild Extensions. Kunen-Paris Forcing. Silver's Forcing.
surability of Ki in ZF. Exercises. Historical Notes.
22.
Real-Valued Measurable Cardinals. Generic
Saturated Ideals. Consistency Strength of Precipitousness. Exercises. Histor¬
ical Notes.
23.
Some Combinatorial Principles. Stationary Sets in Generic Extensions. Pre¬
cipitousness of the Nonstationary Ideal. Saturation of the Nonstationary Ideal.
Reflection. Exercises. Historical Notes.
24.
The Galvin-Hajnal Theorem. Ordinal Functions and Scales. The pcf Theory.
The Structure of pcf. Transitive Generators and Localization. Shelah's Bound
on
25.
The Hierarchy of
and
Uniformization.
Codes. Exercises. Historical Notes.
XII Table of
26.
Random and Cohen reals. Solovay Sets of Reals. The Levy Collapse. Solo-
vay's Theorem. Lebesgue Measurability of
Mathias
Part III. Selected Topics
27.
The Fine Structure Theory. The Principle Ds. The Jensen Hierarchy.
Standard Codes and Standard Parameters. Diamond Principles. Trees in L.
Canonical Functions on
28.
A Nonconstructible
Tree. Consistency of Borel's Conjecture. K+-Aronszajn Trees. Exercises. His¬
torical Notes.
29.
Ramsey Theory. Gaps in
Subsets of
30.
Measure Algebras. Cohen Algebras. Suslin Algebras. Simple Algebras. Infinite
Games on Boolean Algebras. Exercises. Historical Notes.
31.
Definition and Examples. Iteration of Proper Forcing. The Proper Forcing
Axiom. Applications of PFA. Exercises. Historical Notes.
32.
Tl\ Equivalence Relations.
and Perfect Sets.
Exercises. Historical Notes.
33.
Determinacy and Choice. Some Consequences of AD. AD and Large Cardinals.
Projective
34.
Woodin Cardinals.
Forcing. Weakly Homogeneous Trees. Exercises. Historical Notes.
35.
The Core Model. The Covering Theorem for K. The Covering Theorem
for L[U]. The Core Model for Sequences of Measures. Up to a Strong Cardinal.
Inner Models for Woodin Cardinals. Exercises. Historical Notes.
Table
36.
Violating GCH at a Measurable Cardinal. The Singular Cardinal Problem.
Violating
Historical Notes.
37.
RCS iteration of
Reflection Principles. Forcing Axioms. Exercises. Historical Notes.
38.
The Nonstationary Ideal on Mi. Saturation and Precipitousness. Reflection.
Stationary Sets in
Historical Notes.
Bibliography
Notation
Name Index
Index |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Jech, Thomas J. 1944- |
| author_GND | (DE-588)107482673 |
| author_facet | Jech, Thomas J. 1944- |
| author_role | aut |
| author_sort | Jech, Thomas J. 1944- |
| author_variant | t j j tj tjj |
| building | Verbundindex |
| bvnumber | BV022533931 |
| classification_rvk | SK 150 |
| classification_tum | MAT 040f |
| ctrlnum | (OCoLC)255139846 (DE-599)BVBBV022533931 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 3. millenium ed., rev. and expanded; corr. 4. print. |
| format | Book |
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| id | DE-604.BV022533931 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T18:07:36Z |
| indexdate | 2024-07-09T20:59:41Z |
| institution | BVB |
| isbn | 3540440852 9783540440857 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015740474 |
| oclc_num | 255139846 |
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| owner_facet | DE-384 DE-29T DE-703 DE-521 DE-12 DE-11 DE-898 DE-BY-UBR |
| physical | XIII, 769 S. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer monographs in mathematics |
| spelling | Jech, Thomas J. 1944- Verfasser (DE-588)107482673 aut Set theory Thomas Jech 3. millenium ed., rev. and expanded; corr. 4. print. Berlin [u.a.] Springer 2006 XIII, 769 S. txt rdacontent n rdamedia nc rdacarrier Springer monographs in mathematics Mengenlehre Axiomatische Mengenlehre (DE-588)4143743-3 gnd rswk-swf Mengenlehre (DE-588)4074715-3 gnd rswk-swf Mengenlehre (DE-588)4074715-3 s DE-604 Axiomatische Mengenlehre (DE-588)4143743-3 s 1\p DE-604 Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015740474&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 | Jech, Thomas J. 1944- Set theory Mengenlehre Axiomatische Mengenlehre (DE-588)4143743-3 gnd Mengenlehre (DE-588)4074715-3 gnd |
| subject_GND | (DE-588)4143743-3 (DE-588)4074715-3 |
| title | Set theory |
| title_auth | Set theory |
| title_exact_search | Set theory |
| title_exact_search_txtP | Set theory |
| title_full | Set theory Thomas Jech |
| title_fullStr | Set theory Thomas Jech |
| title_full_unstemmed | Set theory Thomas Jech |
| title_short | Set theory |
| title_sort | set theory |
| topic | Mengenlehre Axiomatische Mengenlehre (DE-588)4143743-3 gnd Mengenlehre (DE-588)4074715-3 gnd |
| topic_facet | Mengenlehre Axiomatische Mengenlehre |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015740474&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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