{"product_id":"proofs-and-computations-hardcover","title":"Proofs and Computations - Hardcover","description":"\u003cp\u003eby \u003cb\u003eHelmut Schwichtenberg\u003c\/b\u003e (Author), \u003cb\u003eStanley S. Wainer\u003c\/b\u003e (Author)\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 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.\u003c\/p\u003e\u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 480\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 1.2 x 9.3 x 6.3 IN\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eIllustrated:\u003c\/strong\u003e Yes\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e December 15, 2011\u003c\/div\u003e","brand":"Books by splitShops","offers":[{"title":"Default Title","offer_id":42737016242239,"sku":"9780521517690","price":179.93,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0105\/8226\/1823\/files\/d76a3d8cc6fcec9d9589de8cc3c5599f.webp?v=1765148559","url":"https:\/\/dhlswag.com\/products\/proofs-and-computations-hardcover","provider":"BBB","version":"1.0","type":"link"}