000			01467nam a22001697a 4500
005			20250625095709.0
008			250625b |||||||| |||| 00| 0 eng d
020			_a9780691196411
082			_a511.3 _bSTI
100			_aJohn Stillwell
245			_aReverse Mathematics: _b Proofs from the Inside Out _cJohn Stillwell
260			_bPrinceton _c2018
300			_a182
505			_t1 Historical Introduction 2 Classical Arithmetization 3 Classical Analysis 4 Computability 5 Arithmetization of Computation 6 Arithmetical Comprehension 7 Recursive Comprehension 8 A Bigger Picture
520			_aReverse mathematics is a new field that seeks to find the axioms needed to prove given theorems. Reverse mathematics began as a technical field of mathematical logic, but its main ideas have precedents in the ancient field of geometry and the early twentieth-century field of set theory. This book offers a historical and representative view, emphasizing basic analysis and giving a novel approach to logic. It concludes that mathematics is an arena where theorems cannot always be proved outright, but in which all of their logical equivalents can be found. This creates the possibility of reverse mathematics, where one seeks equivalents that are suitable as axioms. By using a minimum of mathematical logic in a well-motivated way, the book will engage advanced undergraduates and all mathematicians interested in the foundations of mathematics.
942			_2ddc _cBK
999			_c2595 _d2595