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003			BD-SySUS
005			20160413122335.0
007			cr nn 008mamaa
008			130228s2013 sz | s |||| 0|eng d
020			_a9783034802246 _9978-3-0348-0224-6
024	7		_a10.1007/978-3-0348-0224-6 _2doi
050		4	_aQA21-27
072		7	_aPBX _2bicssc
072		7	_aMAT015000 _2bisacsh
082	0	4	_a510.9 _223
100	1		_aHinkis, Arie. _eauthor.
245	1	0	_aProofs of the Cantor-Bernstein Theorem _h[electronic resource] : _bA Mathematical Excursion / _cby Arie Hinkis.
264		1	_aBasel : _bSpringer Basel : _bImprint: Birkhäuser, _c2013.
300			_aXXIII, 429 p. 24 illus., 3 illus. in color. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aScience Networks. Historical Studies ; _v45
505	0		_aPreface. - Part I: Cantor and Dedekind -- Cantor's CBT proof for sets of the power of (II) -- Generalizing Cantor's CBT proof -- CBT in Cantor's 1878 Beitrag -- The theory of inconsistent sets -- Comparability in Cantor's writings -- The scheme of complete disjunction -- Ruptures in the Cantor-Dedekind correspondence -- The inconsistency of Dedekind's infinite set -- Dedekind's proof of CBT -- Part II: The early proofs -- Schröder's Proof of CBT -- Bernstein, Borel and CBT -- Schoenflies' 1900 proof of CBT -- Zermelo's 1901 proof of CBT -- Bernstein's Division Theorem -- Part III: Under the logicist sky -- Russell's 1902 proof of CBT -- The role of CBT in Russell’s Paradox -- Jourdain's 1904 generalization of Grundlagen -- Harward 1905 on Jourdain 1904 -- Poincaré and CBT -- Peano's proof of CBT -- J. Kőnig's strings gestalt -- From kings to graphs -- Jourdain's improvements round -- Zermelo's 1908 proof of CBT -- Korselt's proof of CB -- Proofs of CBT in Principia Mathematica -- The origin of Hausdorff Paradox in BDT -- Part IV: At the Polish school -- Sierpiński's proofs of BDT -- Banach's proof of CBT -- Kuratowski's proof of BDT -- Early fixed-point CBT proofs: Whittaker; Tarski-Knaster -- CBT and BDT for order-types -- Sikorski's proof of CBT for Boolean algebras -- Tarski's proofs of BDT and the inequality-BDT -- Tarski's Fixed-Point Theorem and CBT -- Reichbach's proof of CBT -- Part V: Other ends and beginnings -- Hellmann's proof of CBT -- CBT and intuitionism -- CBT in category theory -- Conclusion -- Bibliography -- Index of names -- Index of subjects.
520			_aThis book offers an excursion through the developmental area of research mathematics. It presents some 40 papers, published between the 1870s and the 1970s, on proofs of the Cantor-Bernstein theorem and the related Bernstein division theorem. While the emphasis is placed on providing accurate proofs, similar to the originals, the discussion is broadened to include aspects that pertain to the methodology of the development of mathematics and to the philosophy of mathematics. Works of prominent mathematicians and logicians are reviewed, including Cantor, Dedekind, Schröder, Bernstein, Borel, Zermelo, Poincaré, Russell, Peano, the Königs, Hausdorff, Sierpinski, Tarski, Banach, Brouwer and several others mainly of the Polish and the Dutch schools. In its attempt to present a diachronic narrative of one mathematical topic, the book resembles Lakatos’ celebrated book Proofs and Refutations. Indeed, some of the observations made by Lakatos are corroborated herein. The analogy between the two books is clearly anything but superficial, as the present book also offers new theoretical insights into the methodology of the development of mathematics (proof-processing), with implications for the historiography of mathematics.
650		0	_aMathematics.
650		0	_aCategory theory (Mathematics).
650		0	_aHomological algebra.
650		0	_aHistory.
650		0	_aMathematical logic.
650	1	4	_aMathematics.
650	2	4	_aHistory of Mathematical Sciences.
650	2	4	_aMathematical Logic and Foundations.
650	2	4	_aCategory Theory, Homological Algebra.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783034802239
830		0	_aScience Networks. Historical Studies ; _v45
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-0348-0224-6
912			_aZDB-2-SMA
942			_2Dewey Decimal Classification _ceBooks
999			_c45207 _d45207