000			03317nam a22004455i 4500
001			978-1-4471-2173-2
003			DE-He213
005			20180115171509.0
007			cr nn 008mamaa
008			130727s2012 xxk| s |||| 0|eng d
020			_a9781447121732 _9978-1-4471-2173-2
024	7		_a10.1007/978-1-4471-2173-2 _2doi
050		4	_aQA8.9-10.3
072		7	_aPBC _2bicssc
072		7	_aPBCD _2bicssc
072		7	_aMAT018000 _2bisacsh
082	0	4	_a511.3 _223
100	1		_aHalbeisen, Lorenz J. _eauthor.
245	1	0	_aCombinatorial Set Theory _h[electronic resource] : _bWith a Gentle Introduction to Forcing / _cby Lorenz J. Halbeisen.
264		1	_aLondon : _bSpringer London : _bImprint: Springer, _c2012.
300			_aXVI, 456 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aSpringer Monographs in Mathematics, _x1439-7382
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.
650		0	_aMathematics.
650		0	_aMathematical logic.
650	1	4	_aMathematics.
650	2	4	_aMathematical Logic and Foundations.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781447121725
830		0	_aSpringer Monographs in Mathematics, _x1439-7382
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4471-2173-2
912			_aZDB-2-SMA
999			_c370403 _d370403