| Description |
1 online resource (x, 142 pages) |
| Physical Medium |
polychrome |
| Description |
text file |
| Summary |
Ever since Paul Cohen's spectacular use of the forcing concept to prove the independence of the continuum hypothesis from the standard axioms of set theory, forcing has been seen by the general mathematical community as a subject of great intrinsic interest but one that is technically so forbidding that it is only accessible to specialists. In the past decade, a series of remarkable solutions to long-standing problems in C*-algebra using set-theoretic methods, many achieved by the author and his collaborators, have generated new interest in this subject. This is the first book aimed at explaining forcing to general mathematicians. It simultaneously makes the subject broadly accessible by explaining it in a clear, simple manner, and surveys advanced applications of set theory to mainstream topics. |
| Bibliography |
Includes bibliographical references and indexes. |
| Contents |
1. Peano arithmetic -- 2. Zermelo-Fraenkel set theory -- 3. Well-ordered sets -- 4. Ordinals -- 5. Cardinals -- 6. Relativization -- 7. Reflection -- 8. Forcing notions -- 9. Generic extensions -- 10. Forcing equality -- 11. The fundamental theorem -- 12. Forcing CH -- 13. Forcing [symbol]CH -- 14. Families of entire functions -- 15. Self-homeomorphisms of [symbols]I* -- 16. Pure sttes on [symbol](H)* -- 17. The diamond principle -- 18. Suslin's problem, I* -- 19. Naimark's problem* -- 20. A stronger diamond -- 21. Whitehead's problem, I* -- 22. Iterated forcing -- 23. Martin's axiom -- 24. Suslin's problem, II* -- 25. Whitehead's problem, II* -- 26. The open coloring axiom -- 27. Self-homeomorphisms of [symbols], II* -- 28. Automorphisms of the Calkin algebra, I* -- 29. Automorphisms of the Calkin algebra, II* -- 30. The multiverse interpretation. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Forcing (Model theory)
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Forcing (Model theory) |
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Set theory.
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Set theory. |
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Axiom of choice.
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Axiom of choice. |
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Continuum hypothesis.
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Continuum hypothesis. |
| Genre/Form |
Electronic books.
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Electronic books.
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| Other Form: |
Print version: Weaver, Nik. Forcing for mathematicians. [Hackensack] New Jersey : World Scientific, 2014 9789814566001 (DLC) 2013047943 (OCoLC)860881611 |
| ISBN |
9789814566018 (electronic book) |
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9814566012 (electronic book) |
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9789814566001 (hardcover ; alkaline paper) |
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9814566004 (hardcover ; alkaline paper) |
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9789814566957 (paperback ; alkaline paper) |
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9814566950 (paperback ; alkaline paper) |
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