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LEADER 00000cam  2200805 a 4500 
001    765949043 
003    OCoLC 
005    20210319100908.5 
006    m     o  d         
007    cr cnu---unuuu 
008    111202s2012    enk     ob    001 0 eng d 
019    776113803|a817057793|a823131684|a824107671|a1058718830
020    9781447121732|q(electronic bk.) 
020    1447121732|q(electronic bk.) 
020    1447121724|q(print) 
020    9781447121725|q(print) 
020    9781447160861|q(print) 
020    144716086X 
020    9781447121749|q(print) 
020    1447121740 
020    |z9781447121725 
024 7  10.1007/978-1-4471-2173-2|2doi 
035    (OCoLC)765949043|z(OCoLC)776113803|z(OCoLC)817057793
037    |bSpringer 
040    GW5XE|beng|epn|cGW5XE|dCOO|dEBLCP|dOCLCQ|dE7B|dN$T|dTPH
049    MAIN 
050  4 QA248|b.H35 2012 
060  4 Online Book 
072  7 PBC|2bicssc 
072  7 MAT|x028000|2bisacsh 
072  7 PBC|2thema 
072  7 PBCD|2thema 
082 04 511.3/22|223 
100 1  Halbeisen, Lorenz J. 
245 10 Combinatorial set theory :|bwith a gentle introduction to 
       forcing /|cLorenz J. Halbeisen. 
260    London ;|aNew York :|bSpringer-Verlag London Ltd.,|c2012. 
300    1 online resource (xvi, 453 pages) 
336    text|btxt|2rdacontent 
337    computer|bc|2rdamedia 
338    online resource|bcr|2rdacarrier 
347    text file 
347    |bPDF 
490 1  Springer monographs in mathematics,|x1439-7382 
504    Includes bibliographical references and index. 
505 0  The 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    This 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    English. 
650  0 Combinatorial set theory. 
650  0 Forcing (Model theory) 
650  7 MATHEMATICS|xSet Theory.|2bisacsh 
650  7 Combinatorial set theory.|2fast|0(OCoLC)fst00868986 
650  7 Forcing (Model theory)|2fast|0(OCoLC)fst00931616 
650 12 Mathematics. 
776 08 |iPrinted edition:|z9781447121725 
830  0 Springer monographs in mathematics. 
990    SpringerLink|bSpringer English/International eBooks 2012 -
       Full Set|c2021-03-19|yMaster record encoding level change
990    SpringerLink|bSpringer English/International eBooks 2012 -
       Full Set|c2018-10-31|yNew collection 
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