{"product_id":"reverse-mathematics-by-john-stillwell-9780691177175","title":"Reverse Mathematics","description":"\u003cdiv class=\"book-description\"\u003e\n\u003cp\u003eThis 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?\u003c\/p\u003e\n\n\u003cp\u003eOnly 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 \u003cem\u003eReverse Mathematics\u003c\/em\u003e, 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. \u003c\/p\u003e\n\n\u003cp\u003eStillwell 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.\u003c\/p\u003e\n\n\u003cp\u003eReverse 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.\u003c\/p\u003e\n\n\u003cp\u003eBy using a minimum of mathematical logic in a well-motivated way, \u003cem\u003eReverse Mathematics\u003c\/em\u003e will engage advanced undergraduates and all mathematicians interested in the foundations of mathematics.\u003c\/p\u003e\n\u003c\/div\u003e","brand":"NewSouth Books","offers":[{"title":"Default Title","offer_id":46854812008684,"sku":"9780691177175","price":67.99,"currency_code":"NZD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0705\/7784\/8556\/files\/9aa09e2ba304df92932c4958248aea1a.jpg?v=1759264629","url":"https:\/\/bookhero.pro\/products\/reverse-mathematics-by-john-stillwell-9780691177175","provider":"Book Hero","version":"1.0","type":"link"}