{"product_id":"proofs-and-computations-9780521517690","title":"Proofs and Computations","description":"\u003cp\u003e • Author(s): Helmut Schwichtenberg | Stanley S. Wainer\u003cbr\u003e • Publisher: Cambridge University Press\u003cbr\u003e • Publisher Imprint: Cambridge University Press\u003cbr\u003e • BISAC: Logic\u003c\/p\u003e\u003cp\u003eDriven 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 Gödel'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.\u003c\/p\u003e","brand":"Cambridge University Press","offers":[{"title":"Hardcover","offer_id":46868327366807,"sku":"9780521517690","price":10090.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9780521517690.webp?v=1769989199","url":"https:\/\/atlanticbooks.com\/products\/proofs-and-computations-9780521517690","provider":"Atlantic Books","version":"1.0","type":"link"}