{"product_id":"the-foundations-of-mathematics-in-the-theory-of-sets-hardback-9780521770347","title":"The Foundations of Mathematics in the Theory of Sets (Hardback) 9780521770347","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eThe Foundations of Mathematics in the Theory of Sets\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eThis 2001 book will appeal to mathematicians and philosophers interested in the foundations of mathematics.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eJohn P. Mayberry (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521770347, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 22 March 2001\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e446 pages\u003cbr\u003e23.7 x 16.3 x 2.7 cm, 0.8 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003eReview of the hardback: ' … this book is thought-provoking … distinctive approach to the twin issues of mathematical ontology and mathematical foundations'. Australasian Journal of Philosophy\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis 2001 book presents a unified approach to the foundations of mathematics in the theory of sets, covering both conventional and finitary (constructive) mathematics. It is based on a philosophical, historical and mathematical analysis of the relation between the concepts of 'natural number' and 'set'. This leads to an investigation of the logic of quantification over the universe of sets and a discussion of its role in second order logic, as well as in the analysis of proof by induction and definition by recursion. The subject matter of the book falls on the borderline between philosophy and mathematics, and should appeal to both philosophers and mathematicians with an interest in the foundations of mathematics.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface\u003cbr\u003e Part I. Preliminaries: 1. The idea of foundations of mathematics\u003cbr\u003e 2. Simple arithmetic\u003cbr\u003e Part II. Basic Set Theory: 3. Semantics, ontology and logic\u003cbr\u003e 4. The principal axioms and definitions of set theory\u003cbr\u003e Part III. Cantorian Set Theory: 5. Cantorian finitism\u003cbr\u003e 6. The axiomatic method\u003cbr\u003e 7. Axiomatic set theory\u003cbr\u003e Part IV. Euclidean Set Theory: 8. Euclidian finitism\u003cbr\u003e 9. The Euclidean theory of cardinality\u003cbr\u003e 10. The theory of simply infinite systems\u003cbr\u003e 11. Euclidean set theory from the Cantorian standpoint\u003cbr\u003e 12. Envoi\u003cbr\u003e Appendices\u003cbr\u003e Bibliography\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Set theory [\u003ca title=\"See our other books on Set theory\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Set%20theory%20%5BPBCH%5D%22\"\u003ePBCH\u003c\/a\u003e], 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], Philosophy [\u003ca title=\"See our other books on Philosophy\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Philosophy%20%5BHP%5D%22\"\u003eHP\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":46004623474968,"sku":"9780521770347","price":122.89,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521770347i_391ea70a-0b5c-430e-8de7-bb1e85ebfe92.jpg?v=1691367760","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/the-foundations-of-mathematics-in-the-theory-of-sets-hardback-9780521770347","provider":"Freshly Printed Books","version":"1.0","type":"link"}