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Proofs and computations:

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Bibliographische Detailangaben
Beteiligte Personen:	Schwichtenberg, Helmut 1942- (VerfasserIn), Wainer, Stanley S. (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Cambridge [u.a.] Cambridge Univ. Press [u.a.] 2012
Ausgabe:	1. publ.
Schriftenreihe:	Perspectives in logic
Schlagwörter:	Rekursionstheorie Beweistheorie
Links:	http://scans.hebis.de/HEBCGI/show.pl?27869657_toc.html http://scans.hebis.de/HEBCGI/show.pl?27869657_kub.html http://scans.hebis.de/HEBCGI/show.pl?27869657_aub.html http://scans.hebis.de/HEBCGI/show.pl?27869657_bio.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024887740&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XIII, 465 S. 23x16x3 cm
ISBN:	9780521517690 0521517699

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Datensatz im Suchindex

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adam_text	Titel: Proofs and computations Autor: Schwichtenberg, Helmut Jahr: 2012 CONTENTS page Preface xi Preliminaries 1 Part 1. Basic proof theory and computability Chapter 1. Logic 5 1.1. Natural deduction 6 1.2. Normalization 20 1.3. Soundness and completeness for tree modeis 44 1.4. Soundness and completeness of the classical fragment 52 1.5. Tait calculus 57 1.6. Notes 59 Chapter 2. Recursion theory 61 2.1. Register machines 61 2.2. Elementary functions 65 2.3. Kleene s normal form theorem 73 2.4. Recursive definitions 78 2.5. Primitive recursion and for-loops 84 2.6. The arithmetical hierarchy 90 2.7. The analytical hierarchy 94 2.8. Recursive type-2 functionals and well-foundedness 98 2.9. Inductive definitions 102 2.10. Notes 110 Chapter 3. Gödel s theorems 113 3.1. IAo(exp) 114 3.2. Gödel numbers 123 3.3. The notion of truth in formal theories 13 3 3.4. Undecidability and incompleteness 135 3.5. Representability 137 3.6. Unprovability of consistency 141 3.7. Notes 145 vii viii Contents Part 2. Provable recursion in classical Systems Chapter 4. The provably recursive Functions of arithmetic 149 4.1. Primitive recursion and IX] 151 4.2. eo-recursion in Peano arithmetic 157 4.3. Ordinal bounds for provable recursion in PA 173 4.4. Independence results for PA 185 4.5. Notes 192 Chapter 5. Accessible recursive Functions, ID tu and nj-CA0 195 5.1. The subrecursive stumblingblock 195 5.2. Accessible recursive functions 199 5.3. Proof-theoretic characterizations of accessibility 215 5.4. ID coandnj-CA0 231 5.5. An independence result: extended Kruskal theorem 237 5.6. Notes 245 Part 3. Constructive logic and complexity Chapter 6. Computability in higher types 249 6.1. Abstract computability via Information Systems 249 6.2. Denotational and operational semantics 266 6.3. Normalization 290 6.4. Computable functionals 296 6.5. Total functionals 304 6.6. Notes 309 Chapter 7. Extracting computational contentfrom proofs 313 7.1. A theory of computable functionals 313 7.2. Realizability Interpretation 327 7.3. Refined ^-translation 352 7.4. Gödel s Dialectica interpretation 367 7.5. Optimal decoration of proofs 380 7.6. Application: Euclid s theorem 388 7.7. Notes 392 Chapter 8. Linear two-sorted arithmetic 395 8.1. Provable recursion and complexity in EA(;) 397 8.2. A two-sorted variant T(;) of Gödel s T 404 8.3. A linear two-sorted variant LT(;) of Gödel s T 412 8.4. Two-sorted Systems A(;),LA(;) 422 8.5. Notes 428 Bibliography 431 Index 457
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spellingShingle	Schwichtenberg, Helmut 1942- Wainer, Stanley S. Proofs and computations Rekursionstheorie (DE-588)4122329-9 gnd Beweistheorie (DE-588)4145177-6 gnd
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title	Proofs and computations
title_auth	Proofs and computations
title_exact_search	Proofs and computations
title_full	Proofs and computations Helmut Schwichtenberg, Stanley S. Wainer
title_fullStr	Proofs and computations Helmut Schwichtenberg, Stanley S. Wainer
title_full_unstemmed	Proofs and computations Helmut Schwichtenberg, Stanley S. Wainer
title_short	Proofs and computations
title_sort	proofs and computations
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