{"text_format":"2","workbook":"xls","n_sheets":1,"sheets":["report2"],"not_rendered":{"charts":0,"images":0,"macros":0,"external_links":1,"defined_names":1,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"run_cost":"one","rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900","formulas":"cached_only"}

{"sheet":"report2","index":0,"n_rows":29,"n_cols":5,"rows_kept":29,"cut":false,"hidden":false,"merged":[[0,2,0,3],[0,4,0,5],[1,2,1,3],[1,4,1,5],[2,2,2,3],[2,4,2,5],[3,2,3,3],[4,2,4,3],[13,2,13,3],[14,2,14,3],[15,2,15,3],[16,2,16,3],[18,2,18,3],[19,2,19,3],[23,2,23,3]],"flags":["formulas_cached_only"]}
[null,"1.","Record Nr.",null,"UNINA9910461496003321"]
[null,null,"Autore",null,"Schwichtenberg Helmut <1942->"]
[null,null,"Titolo",null,"Proofs and computations / / Helmut Schwichtenberg, Stanley S. Wainer [[electronic resource]]"]
[null,null,"Pubbl/distr/stampa",null,"Cambridge : , : Cambridge University Press, , 2012"]
[null,null,"ISBN",null,"1-107-22428-4"]
[{"$nulls":4},"1-280-48485-3"]
[{"$nulls":4},"1-139-22192-2"]
[{"$nulls":4},"9786613579836"]
[{"$nulls":4},"1-139-21710-0"]
[{"$nulls":4},"1-139-21403-9"]
[{"$nulls":4},"1-139-22363-1"]
[{"$nulls":4},"1-139-22020-9"]
[{"$nulls":4},"1-139-03190-2"]
[null,null,"Descrizione fisica",null,"1 online resource (xiii, 465 pages) : digital, PDF file(s)"]
[null,null,"Collana",null,"Perspectives in logic"]
[null,null,"Disciplina",null,"511.352"]
[null,null,"Soggetti",null,"Computable functions"]
[{"$nulls":4},"Proof theory"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Title from publisher's bibliographic system (viewed on 05 Oct 2015)."]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,"Nota di contenuto",null,"1.4. Soundness and completeness of the classical fragment1.4.1. Models.; 1.4.2. Soundness of classical logic.; 1.4.3. Completeness of classical logic.; 1.4.4. Compactness and Löwenheim-Skolem theorems.; 1.5. Tait calculus; 1.6. Notes; Chapter 2: RECURSION THEORY; 2.1. Register machines; 2.1.1. Programs.; 2.1.2. Program constructs.; 2.1.3. Register machine computable functions.; 2.2. Elementary functions; 2.2.1. Definition and simple properties.; 2.2.2. Elementary relations.; 2.2.3. The class ε.; 2.2.4. Closure properties of ε.; 2.2.5. Coding finite lists.; 2.3. Kleene's normal form theorem"]
[{"$nulls":4},"2.3.1. Program numbers.2.3.2. Normal form.; 2.3.3. Σo1-definable relations and μ-recursive functions.; 2.3.4. Computable functions.; 2.3.5. Undecidability of the halting problem.; 2.4. Recursive definitions; 2.4.1. Least fixed points of recursive definitions.; 2.4.2. The principles of finite support and monotonicity, and the effective index property.; 2.4.3. Recursion theorem.; 2.4.4. Recursive programs and partial recursive functions.; 2.4.5. Relativized recursion.; 2.5. Primitive "]
[{"$nulls":4},"recursion and for-loops; 2.5.1. Primitive recursive functions.; 2.5.2. Loop-programs."]
[{"$nulls":4},"2.5.3. Reduction to primitive recursion.2.5.4. A complexity hierarchy for Prim.; 2.6. The arithmetical hierarchy; 2.6.1. Kleene's second recursion theorem.; 2.6.2. Characterization of Σ01-definable and recursive relations.; 2.6.3. Arithmetical relations.; 2.6.4. Closure properties.; 2.6.6. Σ0r-complete relations.; 2.7. The analytical hierarchy; 2.7.1. Analytical relations.; 2.7.2. Closure properties.; 2.7.3. Universal Σ1r+1-definable relations.; 2.7.4. Σ1r-complete relations.; 2.8. Recursive type-2 functionals and well-foundedness; 2.8.1. Computation trees.; 2.8.2. Ordinal assignments"]
[{"$nulls":4},"recursive ordinals."]
[null,null,null,"Sommario/riassunto","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 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."]