{"product_id":"subsystems-of-second-order-arithmetic-paperback-9780521150149","title":"Subsystems of Second Order Arithmetic (Paperback) 9780521150149","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eSubsystems of Second Order Arithmetic\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eThrough a series of case studies, this volume examines these axioms to prove particular theorems in core mathematical areas.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eStephen G. Simpson (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521150149, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback, published 18 February 2010\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e464 pages\u003cbr\u003e23.4 x 15.6 x 2.4 cm, 0.65 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eAlmost 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.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eList of tables\u003cbr\u003e Preface\u003cbr\u003e Acknowledgements\u003cbr\u003e 1. Introduction\u003cbr\u003e Part I. Development of Mathematics within Subsystems of Z2: 2. Recursive comprehension\u003cbr\u003e 3. Arithmetical comprehension\u003cbr\u003e 4. Weak König's lemma\u003cbr\u003e 5. Arithmetical transfinite recursion\u003cbr\u003e 6. ?11 comprehension\u003cbr\u003e Part II. Models of Subsystems of Z2: 7. ?-models\u003cbr\u003e 8. ?-models\u003cbr\u003e 9. Non-?-models\u003cbr\u003e Part III. Appendix: 10. Additional results\u003cbr\u003e Bibliography\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46004197032216,"sku":"9780521150149","price":43.87,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521884396_377e3df1-e794-4271-b2f9-db9c559ef38d.jpg?v=1691372634","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/subsystems-of-second-order-arithmetic-paperback-9780521150149","provider":"Freshly Printed Books","version":"1.0","type":"link"}