{"product_id":"proof-analysis-a-contribution-to-hilberts-last-problem-hardback-9781107008953","title":"Proof Analysis; A Contribution to Hilbert's Last Problem (Hardback) 9781107008953","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eProof Analysis\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eA Contribution to Hilbert's Last Problem\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003ePresents a new way of applying the methods of proof theory to axiomatic theories and systems of philosophical logic.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eSara Negri (Author), Jan von Plato (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781107008953, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 29 September 2011\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e278 pages\u003cbr\u003e25.4 x 18 x 1.8 cm, 0.72 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\"...provide a substantial contribution to the development of proof theory in mathematics.... The book covers a lot of useful material in a concise, efficient and very clearly structured manner. The chapters are written with a palpable intention to show how vast the applicability of the methods is. The results are uniform, general and require a high-level preparation in many different fields. This book can be seen as the stimulating continuation of the authors’ introductory book Structural Proof Theory...\"  \u003cbr\u003e\u003cb\u003e--F. Poggiolesi, Institut d'Histoire et Philosophie des Sciences, Paris, France, History and Philosophy of Logic\u003c\/b\u003e\u003cbr\u003e\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis book continues from where the authors' previous book, Structural Proof Theory, ended. It presents an extension of the methods of analysis of proofs in pure logic to elementary axiomatic systems and to what is known as philosophical logic. A self-contained brief introduction to the proof theory of pure logic is included that serves both the mathematically and philosophically oriented reader. The method is built up gradually, with examples drawn from theories of order, lattice theory and elementary geometry. The aim is, in each of the examples, to help the reader grasp the combinatorial behaviour of an axiom system, which typically leads to decidability results. The last part presents, as an application and extension of all that precedes it, a proof-theoretical approach to the Kripke semantics of modal and related logics, with a great number of new results, providing essential reading for mathematical and philosophical logicians.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePrologue: Hilbert's Last Problem\u003cbr\u003e 1. Introduction\u003cbr\u003e Part I. Proof Systems Based on Natural Deduction: 2. Rules of proof: natural deduction\u003cbr\u003e 3. Axiomatic systems\u003cbr\u003e 4. Order and lattice theory\u003cbr\u003e 5. Theories with existence axioms\u003cbr\u003e Part II. Proof Systems Based on Sequent Calculus: 6. Rules of proof: sequent calculus\u003cbr\u003e 7. Linear order\u003cbr\u003e Part III. Proof Systems for Geometric Theories: 8. Geometric theories\u003cbr\u003e 9. Classical and intuitionistic axiomatics\u003cbr\u003e 10. Proof analysis in elementary geometry\u003cbr\u003e Part IV. Proof Systems for Nonclassical Logics: 11. Modal logic\u003cbr\u003e 12. Quantified modal logic, provability logic, and so on\u003cbr\u003e Bibliography\u003cbr\u003e Index of names\u003cbr\u003e Index of subjects.\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], Philosophy of mathematics [\u003ca title=\"See our other books on Philosophy of mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Philosophy%20of%20mathematics%20%5BPBB%5D%22\"\u003ePBB\u003c\/a\u003e], Philosophy: logic [\u003ca title=\"See our other books on Philosophy: logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Philosophy:%20logic%20%5BHPL%5D%22\"\u003eHPL\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":46265455903000,"sku":"9781107008953","price":90.59,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9781107008953i.jpg?v=1692023045","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/proof-analysis-a-contribution-to-hilberts-last-problem-hardback-9781107008953","provider":"Freshly Printed Books","version":"1.0","type":"link"}