{"product_id":"proofs-and-computations-9780521517690","title":"Proofs and Computations","description":"Driven by the question, 'What is the computational content of a (formal) proof?', this book studies fundamental interactions between proof theory and computability. It provides a unique self-contained text for advanced students and researchers in mathematical logic and computer science. Part I covers basic proof theory, computability and G del's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to Π11-CA0. Ordinal analysis and the (Schwichtenberg-Wainer) subrecursive hierarchies play a central role and are used in proving the 'modified finite Ramsey' and 'extended Kruskal' independence results for PA and Π11-CA0. Part III develops the theoretical underpinnings of the first author's proof assistant MINLOG. Three chapters cover higher-type computability via information systems, a constructive theory TCF of computable functionals, realizability, Dialectica interpretation, computationally significant quantifiers and connectives and polytime complexity in a two-sorted, higher-type arithmetic with linear logic.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Helmut Schwichtenberg, Stanley S. Wainer\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Cambridge University Press\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 12\/31\/2011\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 480\u003cbr\u003e\u003cb\u003eBinding Type:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.90lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.30h x 6.30w x 1.20d\u003cbr\u003e\u003cb\u003eISBN:\u003c\/b\u003e 9780521517690\u003cbr\u003e\u003cp\u003e\u003cb\u003eAbout the Author\u003c\/b\u003e\u003cbr\u003e\u003cb\u003e\u003ci\u003eWainer, Stanley S.:\u003c\/i\u003e\u003c\/b\u003e - Stanley S. Wainer is an Emeritus Professor of Mathematics at the University of Leeds and a past-President of the British Logic Colloquium.\u003cb\u003e\u003ci\u003eSchwichtenberg, Helmut:\u003c\/i\u003e\u003c\/b\u003e - Helmut Schwichtenberg is an Emeritus Professor of Mathematics at Ludwig-Maximilians-Universität München. He has recently developed the 'proof-assistant' MINLOG, a computer-implemented logic system for proof\/program development and extraction of computational content.\u003c\/p\u003e","brand":"Cambridge University Press","offers":[{"title":"Hardcover","offer_id":40031404785779,"sku":"9.78E+12","price":88.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0555\/9255\/0515\/products\/img_a13e783b-6031-40b2-bcec-b74c1523fbab.jpg?v=1650840764","url":"https:\/\/bookstorenmore.com\/products\/proofs-and-computations-9780521517690","provider":"Bookstore N More","version":"1.0","type":"link"}