000			07406cam a2200757 i 4500
001			on1012849815
003			OCoLC
005			20220908100133.0
006			m o d
007			cr |||||||||||
008			171124s2018 njua ob 001 0 eng d
040			_aIDEBK _beng _erda _epn _cIDEBK _dN$T _dEBLCP _dYDX _dCNCGM _dMNW _dMUU _dIDB _dNRC _dINT _dDEGRU _dAU@ _dTSC _dOCLCQ _dWYU _dOCLCQ _dJSTOR _dOCLCQ _dMM9 _dUX1 _dOCLCQ _dIEEEE _dOCLCQ _dOCLCO
066			_c(S
019			_a1162046061 _a1175629450
020			_a1400889030 _q(electronic bk.)
020			_a9781400889037
020			_z9780691177175 _q(hardcover _qalk. paper)
020			_z0691177171 _q(hardcover _qalk. paper)
029	1		_aAU@ _b000061388128
029	1		_aGBVCP _b1011003759
029	1		_aAU@ _b000062004912
029	1		_aAU@ _b000062577688
029	1		_aAU@ _b000065054106
029	1		_aAU@ _b000067043333
035			_a(OCoLC)1012849815 _z(OCoLC)1162046061 _z(OCoLC)1175629450
037			_a1050470 _bMIL
037			_a22573/ctvc66xk3 _bJSTOR
037			_a9452339 _bIEEE
050		4	_aQA9.25
072		7	_aMAT _x000000 _2bisacsh
072		7	_aMAT _x015000 _2bisacsh
072		7	_aMAT _x018000 _2bisacsh
072		7	_aMAT _x034000 _2bisacsh
072		7	_aSCI _x034000 _2bisacsh
082	0	4	_a511.3 _223
084			_aMAT015000 _aMAT000000 _aMAT018000 _aSCI034000 _2bisacsh
049			_aMAIN
100	1		_aStillwell, John, _eauthor. _965032
245	1	0	_aReverse mathematics : _bproofs from the inside out / _cJohn Stillwell.
264		1	_aPrinceton : _bPrinceton University Press, _c[2018]
264		4	_c�2018
300			_a1 online resource (xiii, 182 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
504			_aIncludes bibliographical references and index.
505	0		_6880-01 _aHistorical introduction -- Classical arithmetization -- Classical analysis -- Computability -- Arithmetization of computation -- Arithmetical comprehension -- Recursive comprehension -- A bigger picture.
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."-- _cProvided by publisher
588	0		_aOnline resource; title from electronic title page (EBSCOHost, viewed March 14, 2018).
590			_aIEEE _bIEEE Xplore Princeton University Press eBooks Library
650		0	_aReverse mathematics. _965033
650		6	_aMath�ematiques �a rebours. _965034
650		7	_aMATHEMATICS _xGeneral. _2bisacsh _94635
650		7	_aReverse mathematics. _2fast _0(OCoLC)fst01737141 _965033
655		4	_aElectronic books. _93294
776	0	8	_iPrint version: _aStillwell, John. _tReverse mathematics. _dPrinceton, New Jersey : Princeton University Press, [2018] _z9780691177175 _w(DLC) 2017025264 _w(OCoLC)983825003
856	4	0	_uhttps://ieeexplore.ieee.org/servlet/opac?bknumber=9452339
880	0	0	_6505-01/(S _gMachine generated contents note: _g1. _tHistorical Introduction -- _g1.1. _tEuclid and the Parallel Axiom -- _g1.2. _tSpherical and Non-Euclidean Geometry -- _g1.3. _tVector Geometry -- _g1.4. _tHilbert's Axioms -- _g1.5. _tWell-ordering and the Axiom of Choice -- _g1.6. _tLogic and Computability -- _g2. _tClassical Arithmetization -- _g2.1. _tFrom Natural to Rational Numbers -- _g2.2. _tFrom Rationals to Reals -- _g2.3. _tCompleteness Properties of R -- _g2.4. _tFunctions and Sets -- _g2.5. _tContinuous Functions -- _g2.6. _tPeano Axioms -- _g2.7. _tLanguage of PA -- _g2.8. _tArithmetically Definable Sets -- _g2.9. _tLimits of Arithmetization -- _g3. _tClassical Analysis -- _g3.1. _tLimits -- _g3.2. _tAlgebraic Properties of Limits -- _g3.3. _tContinuity and Intermediate Values -- _g3.4. _tBolzano-Weierstrass Theorem -- _g3.5. _tHeine-Borel Theorem -- _g3.6. _tExtreme Value Theorem -- _g3.7. _tUniform Continuity -- _g3.8. _tCantor Set -- _g3.9. _tTrees in Analysis -- _g4. _tComputability -- _g4.1. _tComputability and Church's Thesis -- _g4.2. _tHalting Problem -- _g4.3. _tComputably Enumerable Sets -- _g4.4. _tComputable Sequences in Analysis -- _g4.5. _tComputable Tree with No Computable Path -- _g4.6. _tComputability and Incompleteness -- _g4.7. _tComputability and Analysis -- _g5. _tArithmetization of Computation -- _g5.1. _tFormal Systems -- _g5.2. _tSmullyan's Elementary Formal Systems -- _g5.3. _tNotations for Positive Integers -- _g5.4. _tTuring's Analysis of Computation -- _g5.5. _tOperations on EFS-Generated Sets -- _g5.6. _tGenerating (SV(B01 Sets -- _g5.7. _tEFS for (SV(B01 Relations -- _g5.8. _tArithmetizing Elementary Formal Systems -- _g5.9. _tArithmetizing Computable Enumeration -- _g5.10. _tArithmetizing Computable Analysis -- _g6. _tArithmetical Comprehension -- _g6.1. _tAxiom System ACA0 -- _g6.2. _t(SV(B01 and Arithmetical Comprehension -- _g6.3. _tCompleteness Properties in ACA0 -- _g6.4. _tArithmetization of Trees -- _g6.5. _tKonig Infinity Lemma -- _g6.6. _tRamsey Theory -- _g6.7. _tSome Results from Logic -- _g6.8. _tPeano Arithmetic in ACA0 -- _g7. _tRecursive Comprehension -- _g7.1. _tAxiom System RCA0 -- _g7.2. _tReal Numbers and Continuous Functions -- _g7.3. _tIntermediate Value Theorem -- _g7.4. _tCantor Set Revisited -- _g7.5. _tFrom Heine-Borel to Weak Konig Lemma -- _g7.6. _tFrom Weak Konig Lemma to Heine-Borel -- _g7.7. _tUniform Continuity -- _g7.8. _tFrom Weak Konig to Extreme Value -- _g7.9. _tTheorems of WKL0 -- _g7.10. _tWKL0, ACA0, and Beyond -- _g8. _tBigger Picture -- _g8.1. _tConstructive Mathematics -- _g8.2. _tPredicate Logic -- _g8.3. _tVarieties of Incompleteness -- _g8.4. _tComputability -- _g8.5. _tSet Theory -- _g8.6. _tConcepts of "Depth."
938			_aDe Gruyter _bDEGR _n9781400889037
938			_aYBP Library Services _bYANK _n14643228
938			_aEBL - Ebook Library _bEBLB _nEBL5199840
938			_aProQuest MyiLibrary Digital eBook Collection _bIDEB _ncis39138779
938			_aEBSCOhost _bEBSC _n1550094
942			_cEBK
994			_a92 _bINTKS
999			_c81391 _d81391