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Record Nr. |
UNINA9910299960803321 |
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Autore |
Schindler Ralf |
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Titolo |
Set Theory : Exploring Independence and Truth / / by Ralf Schindler |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Springer, , 2014 |
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ISBN |
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Edizione |
[1st ed. 2014.] |
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Descrizione fisica |
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1 online resource (335 p.) |
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Collana |
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Universitext, , 0172-5939 |
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Disciplina |
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Soggetti |
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Logic, Symbolic and mathematical |
Mathematical Logic and Foundations |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di contenuto |
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Naive set theory -- Axiomatic set theory -- Ordinals -- Cardinals -- Constructability -- Forcing -- Descriptive set theory -- Solovay’s model -- The Raisonnier filter -- Measurable cardinals -- 0# and Jensen’s Covering Lemma -- Analytic and full determinacy -- Projective determinacy. |
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Sommario/riassunto |
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This textbook gives an introduction to axiomatic set theory and examines the prominent questions that are relevant in current research in a manner that is accessible to students. Its main theme is the interplay of large cardinals, inner models, forcing, and descriptive set theory. The following topics are covered: • Forcing and constructability • The Solovay-Shelah Theorem i.e. the equiconsistency of ‘every set of reals is Lebesgue measurable’ with one inaccessible cardinal • Fine structure theory and a modern approach to sharps • Jensen’s Covering Lemma • The equivalence of analytic determinacy with sharps • The theory of extenders and iteration trees • A proof of projective determinacy from Woodin cardinals. Set Theory requires only a basic knowledge of mathematical logic and will be suitable for advanced students and researchers. |
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