1.

Record Nr.

UNINA9910299960803321

Autore

Schindler Ralf

Titolo

Set Theory : Exploring Independence and Truth / / by Ralf Schindler

Pubbl/distr/stampa

Cham : , : Springer International Publishing : , : Imprint : Springer, , 2014

ISBN

3-319-06725-7

Edizione

[1st ed. 2014.]

Descrizione fisica

1 online resource (335 p.)

Collana

Universitext, , 0172-5939

Disciplina

511.3

Soggetti

Logic, Symbolic and mathematical

Mathematical Logic and Foundations

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di contenuto

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.

Sommario/riassunto

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.