000			02841cam a22003498i 4500
001			19658571
003			IIITD
005			20210206170654.0
008			170523s2018 nju b 001 0 eng
010			_a 2017025264
020			_a9780691177175
040			_aDLC _beng _erda _cDLC
042			_apcc
050	0	0	_aQA9.25 _b.S75 2018
082	0	0	_a511.3 _223 _bSTI-R
084			_aMAT015000 _aMAT000000 _aMAT018000 _aSCI034000 _2bisacsh
100	1		_aStillwell, John
245	1	0	_aReverse mathematics : _bproofs from the inside out _cby John Stillwell.
260			_aPrinceton : _bPrinceton University Press, _c2018.
263			_a1712
300			_axiii, 182 p. : _bill. ; _c25 cm.
504			_aIncludes bibliographical references and index.
520			_a" This book presents reverse mathematics to a general mathematical audience for the first time. Reverse mathematics is a new field that answers some old questions. In the two thousand years that mathematicians have been deriving theorems from axioms, it has often been asked: which axioms are needed to prove a given theorem? Only in the last two hundred years have some of these questions been answered, and only in the last forty years has a systematic approach been developed. In Reverse Mathematics, John Stillwell gives a representative view of this field, emphasizing basic analysis--finding the "right axioms" to prove fundamental theorems--and giving a novel approach to logic. Stillwell introduces reverse mathematics historically, describing the two developments that made reverse mathematics possible, both involving the idea of arithmetization. The first was the nineteenth-century project of arithmetizing analysis, which aimed to define all concepts of analysis in terms of natural numbers and sets of natural numbers. The second was the twentieth-century arithmetization of logic and computation. Thus arithmetic in some sense underlies analysis, logic, and computation. Reverse mathematics exploits this insight by viewing analysis as arithmetic extended by axioms about the existence of infinite sets. Remarkably, only a small number of axioms are needed for reverse mathematics, and, for each basic theorem of analysis, Stillwell finds the "right axiom" to prove it. By using a minimum of mathematical logic in a well-motivated way, Reverse Mathematics will engage advanced undergraduates and all mathematicians interested in the foundations of mathematics. "--
650		0	_aReverse mathematics.
650		7	_aMATHEMATICS / History & Philosophy. _2bisacsh
650		7	_aMATHEMATICS / General. _2bisacsh
650		7	_aMATHEMATICS / Logic. _2bisacsh
650		7	_aSCIENCE / History. _2bisacsh
906			_a7 _bcbc _corignew _d1 _eecip _f20 _gy-gencatlg
942			_2ddc _cBK _01
999			_c24091 _d24091