03040nam 22006015 450 991029996080332120200706053107.03-319-06725-710.1007/978-3-319-06725-4(CKB)3710000000119138(EBL)1731143(SSID)ssj0001247359(PQKBManifestationID)11698911(PQKBTitleCode)TC0001247359(PQKBWorkID)11193204(PQKB)10180633(DE-He213)978-3-319-06725-4(MiAaPQ)EBC6314269(MiAaPQ)EBC1731143(Au-PeEL)EBL1731143(CaPaEBR)ebr10983235(OCoLC)881431325(PPN)178783935(EXLCZ)99371000000011913820140522d2014 u| 0engur|n|---|||||txtccrSet Theory Exploring Independence and Truth /by Ralf Schindler1st ed. 2014.Cham :Springer International Publishing :Imprint: Springer,2014.1 online resource (335 p.)Universitext,0172-5939Description based upon print version of record.3-319-06724-9 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.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.Universitext,0172-5939Logic, Symbolic and mathematicalMathematical Logic and Foundationshttps://scigraph.springernature.com/ontologies/product-market-codes/M24005Logic, Symbolic and mathematical.Mathematical Logic and Foundations.511.3Schindler Ralfauthttp://id.loc.gov/vocabulary/relators/aut524636MiAaPQMiAaPQMiAaPQBOOK9910299960803321Set theory821859UNINA