000			02219nam a22003738i 4500
001			CR9780511581007
003			UkCbUP
005			20200124160234.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			090604s2009||||enk o ||1 0|eng|d
020			_a9780511581007 (ebook)
020			_z9780521884396 (hardback)
020			_z9780521150149 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA9.7 _b.S537 2009
082	0	0	_a511.3 _222
100	1		_aSimpson, Stephen G. _q(Stephen George), _d1945- _eauthor.
245	1	0	_aSubsystems of second order arithmetic / _cStephen G. Simpson.
250			_aSecond edition.
264		1	_aCambridge : _bCambridge University Press, _c2009.
300			_a1 online resource (xvi, 444 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aPerspectives in logic
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
520			_aAlmost all of the problems studied in this book are motivated by an overriding foundational question: What are the appropriate axioms for mathematics? Through a series of case studies, these axioms are examined to prove particular theorems in core mathematical areas such as algebra, analysis, and topology, focusing on the language of second-order arithmetic, the weakest language rich enough to express and develop the bulk of mathematics. In many cases, if a mathematical theorem is proved from appropriately weak set existence axioms, then the axioms will be logically equivalent to the theorem. Furthermore, only a few specific set existence axioms arise repeatedly in this context, which in turn correspond to classical foundational programs. This is the theme of reverse mathematics, which dominates the first half of the book. The second part focuses on models of these and other subsystems of second-order arithmetic.
650		0	_aPredicate calculus.
710	2		_aAssociation for Symbolic Logic, _eissuing body.
776	0	8	_iPrint version: _z9780521884396
830		0	_aPerspectives in logic.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511581007
999			_c517906 _d517904