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Bibliographic Details
Main Author:	Jech, Thomas J. 1944- (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2003
Edition:	3. millenium ed, rev. and expanded
Series:	Springer monographs in mathematics
Subjects:	Mengenlehre Set theory Axiomatische Mengenlehre
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009959885&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Item Description:	Hier auch später erschienene, unveränderte Nachdrucke
Physical Description:	XIII, 769 S.
ISBN:	3540440852 9783540440857

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Record in the Search Index

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adam_text	Table of Contents Part I. Basic Set Theory 1. Axioms of Set Theory 3 Axioms of Zermelo Praenkel. Why Axiomatic Set Theory? Language of Set Theory, Formulas. Classes. Extensionality. Pairing. Separation Schema. Union. Power Set. Infinity. Replacement Schema. Exercises. Historical Notes. 2. Ordinal Numbers 17 Linear and Partial Ordering. Well Ordering. Ordinal Numbers. Induction and Recursion. Ordinal Arithmetic. Well Founded Relations. Exercises. Historical Notes. 3. Cardinal Numbers 27 Cardinality. Alephs. The Canonical Well Ordering of a x a. Cofinality. Ex¬ ercises. Historical Notes. 4. Real Numbers 37 The Cardinality of the Continuum. The Ordering of R. Suslin s Problem. The Topology of the Real Line. Borel Sets. Lebesgue Measure. The Baire Space. Polish Spaces. Exercises. Historical Notes. 5. The Axiom of Choice and Cardinal Arithmetic 47 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 Axiom of Regularity 63 The Cumulative Hierarchy of Sets. e Induction. Well Founded Relations. The Bernays Godel Axiomatic Set Theory. Exercises. Historical Notes. 7. Filters, Ultrafilters and Boolean Algebras 73 Filters and Ultrafilters. Ultrafilters on w. K Complete Filters and Ideals. 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. Stationary Sets 91 Closed Unbounded Sets. Mahlo Cardinals. Normal Filters. Silver s Theo¬ rem. A Hierarchy of Stationary Sets. The Closed Unbounded Filter on PK(X). Exercises. Historical Notes. 9. Combinatorial Set Theory 107 Partition Properties. Weakly Compact Cardinals. Trees. Almost Disjoint Sets and Functions. The Tree Property and Weakly Compact Cardinals. Ramsey Cardinals. Exercises. Historical Notes. 10. Measurable Cardinals 125 The Measure Problem. Measurable and Real Valued Measurable Cardinals. Measurable Cardinals. Normal Measures. Strongly Compact and Supercom pact Cardinals. Exercises. Historical Notes. 11. Borel and Analytic Sets 139 Borel Sets. Analytic Sets. The Suslin Operation A.. The Hierarchy of Projective Sets. Lebesgue Measure. The Property of Baire. Analytic Sets: Measure, Category, and the Perfect Set Property. Exercises. Historical Notes. 12. Models of Set Theory 155 Review of Model Theory. Godel s Theorems. Direct Limits of Models. Re¬ duced Products and Ultraproducts. Models of Set Theory and Relativization. Relative Consistency. Transitive Models and Ao Formulas. Consistency of the Axiom of Regularity. Inaccessibility of Inaccessible Cardinals. Reflection Principle. Exercises. Historical Notes. Part II. Advanced Set Theory 13. Constructible Sets 175 The Hierarchy of Constructible Sets. Godel Operations. Inner Models of ZF. 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 201 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. Applications of Forcing 225 Cohen Reals. Adding Subsets of Regular Cardinals. The K Chain Condition. 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 of Contents XI 16. Iterated Forcing and Martin s Axiom 267 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. Large Cardinals 285 Ultrapowers and Elementary Embeddings. Weak Compactness. Indescribabil ity. Partitions and Models. Exercises. Historical Notes. 18. Large Cardinals and L 311 Silver Indiscernibles. Models with Indiscernibles. Proof of Silver s Theorem and 0 . Elementary Embeddings of L. Jensen s Covering Theorem. Exercises. Historical Notes. 19. Iterated Ultrapowers and L[U] 339 The Model L[U]. Iterated Ultrapowers. Representation of Iterated Ultrapow¬ ers. Uniqueness of the Model L[D]. Indiscernibles for L[D . General Iterations. The Mitchell Order. The Models L[U]. Exercises. Historical Notes. 20. Very Large Cardinals 365 Strongly Compact Cardinals. Supercompact Cardinals. Beyond Supercom pactness. Extenders and Strong Cardinals. Exercises. Historical Notes. 21. Large Cardinals and Forcing 389 Mild Extensions. Kunen Paris Forcing. Silver s Forcing. Prikry Forcing. Mea surability of Ni in ZF. Exercises. Historical Notes. 22. Saturated Ideals 409 Real Valued Measurable Cardinals. Generic Ultrapowers. Precipitous Ideals. Saturated Ideals. Consistency Strength of Precipitousness. Exercises. Histor¬ ical Notes. 23. The Nonstationary Ideal 441 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 Singular Cardinal Problem 457 The Galvin Hajnal Theorem. Ordinal Functions and Scales. The pcf Theory. The Structure of pcf. Transitive Generators and Localization. Shelah s Bound on 2* . Exercises. Historical Notes. 25. Descriptive Set Theory 479 The Hierarchy of Projective Sets, n} Sets. Trees, Well Founded Relations and K Suslin Sets. £2 Sets. Projective Sets and Constructibility. Scales and Uniformization. £2 Well Orderings and Eg Well Founded Relations. Borel Codes. Exercises. Historical Notes. XII Table of Contents 26. The Real Line 511 Random and Cohen reals. Solovay Sets of Reals. The Levy Collapse. Solo vay s Theorem. Lebesgue Measurability of S2 Sets. Ramsey Sets of Reals and Mathias Forcing. Measure and Category. Exercises. Historical Notes. Part III. Selected Topics 27. Combinatorial Principles in I 545 The Fine Structure Theory. The Principle ?«. The Jensen Hierarchy. Projecta, Standard Codes and Standard Parameters. Diamond Principles. Trees in L. Canonical Functions on uii. Exercises. Historical Notes. 28. More Applications of Forcing 557 A Nonconstructible A3 Real. Namba Forcing. A Cohen Real Adds a Suslin Tree. Consistency of Borel s Conjecture. K+ Aronszajn Trees. Exercises. His¬ torical Notes. 29. More Combinatorial Set Theory 573 Ramsey Theory. Gaps in u . The Open Coloring Axiom. Almost Disjoint Subsets of wj. Functions from wi into w. Exercises. Historical Notes. 30. Complete Boolean Algebras 585 Measure Algebras. Cohen Algebras. Suslin Algebras. Simple Algebras. Infinite Games on Boolean Algebras. Exercises. Historical Notes. 31. Proper Forcing 601 Definition and Examples. Iteration of Proper Forcing. The Proper Forcing Axiom. Applications of PFA. Exercises. Historical Notes. 32. More Descriptive Set Theory 615 III Equivalence Relations. S\| Equivalence Relations. Constructible Reals and Perfect Sets. Projective Sets and Large Cardinals. Universally Baire sets. Exercises. Historical Notes. 33. Determinacy 627 Determinacy and Choice. Some Consequences of AD. AD and Large Cardinals. Projective Determinacy. Consistency of AD. Exercises. Historical Notes. 34. Supercompact Cardinals and the Real Line 647 Woodin Cardinals. Semiproper Forcing. The Model L(R). Stationary Tower Forcing. Weakly Homogeneous Trees. Exercises. Historical Notes. 35. Inner Models for Large Cardinals 659 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 of Contents XIII 36. Forcing and Large Cardinals 669 Violating GCH at a Measurable Cardinal. The Singular Cardinal Problem. Violating SCH at Ku,. Radin Forcing. Stationary Tower Forcing. Exercises. Historical Notes. 37. Martin s Maximum 681 RCS iteration of semiproper forcing. Consistency of MM. Applications of MM. Reflection Principles. Forcing Axioms. Exercises. Historical Notes. 38. More on Stationary Sets 695 The Nonstationary Ideal on Ni. Saturation and Precipitousness. Reflection. Stationary Sets in PK(A). Mutually Stationary Sets. Weak Squares. Exercises. Historical Notes. Bibliography 707 Notation 733 Name Index 743 Index 749
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isbn	3540440852 9783540440857
language	English
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spellingShingle	Jech, Thomas J. 1944- Set theory Mengenlehre Set theory 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_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 Set theory Axiomatische Mengenlehre (DE-588)4143743-3 gnd Mengenlehre (DE-588)4074715-3 gnd
topic_facet	Mengenlehre Set theory Axiomatische Mengenlehre
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work_keys_str_mv	AT jechthomasj settheory

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