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008 111202s2012 enk ob 001 0 eng d
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020 $a9781447121732$q(electronic bk.)
020 $a1447121732$q(electronic bk.)
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020 $z9781447121725
024 7 $a10.1007/978-1-4471-2173-2$2doi
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037 $bSpringer
050 4 $aQA248$b.H35 2012
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082 04 $a511.3/22$223
100 1 $aHalbeisen, Lorenz J.
245 10 $aCombinatorial set theory :$bwith a gentle introduction to forcing /$cLorenz J. Halbeisen.
260 $aLondon ;$aNew York :$bSpringer-Verlag London Ltd.,$c©2012.
300 $a1 online resource (xvi, 453 pages)
336 $atext$btxt$2rdacontent
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347 $bPDF
490 1 $aSpringer monographs in mathematics,$x1439-7382
504 $aIncludes bibliographical references and index.
505 0 $aThe Setting -- Overture: Ramsey's Theorem -- The Axioms of Zermelo-Fraenkel Set Theory -- Cardinal Relations in ZF only -- The Axiom of Choice -- How to Make Two Balls from One -- Models of Set Theory with Atoms -- Twelve Cardinals and their Relations -- The Shattering Number Revisited -- Happy Families and their Relatives -- Coda: A Dual Form of Ramsey's Theorem -- The Idea of Forcing -- Martin's Axiom -- The Notion of Forcing -- Models of Finite Fragments of Set Theory -- Proving Unprovability -- Models in which AC Fails -- Combining Forcing Notions -- Models in which p = c -- Properties of Forcing Extensions -- Cohen Forcing Revisited -- Silver-Like Forcing Notions -- Miller Forcing -- Mathias Forcing -- On the Existence of Ramsey Ultrafilters -- Combinatorial Properties of Sets of Partitions -- Suite.
520 $aThis book provides a self-contained introduction to modern set theory and also opens up some more advanced areas of current research in this field. The first part offers an overview of classical set theory wherein the focus lies on the axiom of choice and Ramsey theory. In the second part, the sophisticated technique of forcing, originally developed by Paul Cohen, is explained in great detail. With this technique, one can show that certain statements, like the continuum hypothesis, are neither provable nor disprovable from the axioms of set theory. In the last part, some topics of classical set theory are revisited and further developed in the light of forcing. The notes at the end of each chapter put the results in a historical context, and the numerous related results and the extensive list of references lead the reader to the frontier of research. This book will appeal to all mathematicians interested in the foundations of mathematics, but will be of particular use to graduates in this field.
546 $aEnglish.
650 0 $aCombinatorial set theory.
650 0 $aForcing (Model theory)
650 0 $aMathematics.
650 12 $aMathematics
650 6 $aThéorie combinatoire des ensembles.
650 6 $aForcing (Théorie des modèles)
650 6 $aMathématiques.
650 7 $aMATHEMATICS$xSet Theory.$2bisacsh
650 7 $aMathematics.$2fast$0(OCoLC)fst01012163
650 7 $aCombinatorial set theory.$2fast$0(OCoLC)fst00868986
650 7 $aForcing (Model theory)$2fast$0(OCoLC)fst00931616
655 0 $aElectronic books.
655 4 $aElectronic books.
776 08 $iPrinted edition:$z9781447121725
830 0 $aSpringer monographs in mathematics.
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