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Proof and computations / / Helmut Schwichtenberg, Stanley S. Wainer
| Proof and computations / / Helmut Schwichtenberg, Stanley S. Wainer |
| Autore | Schwichtenberg Helmut <1942-> |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Cambridge, : Cambridge University Press, 2012 |
| Descrizione fisica | 1 online resource (xiii, 465 pages) : digital, PDF file(s) |
| Disciplina | 511.352 |
| Altri autori (Persone) | WainerS. S |
| Collana | Perspectives in logic |
| Soggetto topico |
Computable functions
Proof theory |
| ISBN |
1-107-22428-4
1-280-48485-3 1-139-22192-2 9786613579836 1-139-21710-0 1-139-21403-9 1-139-22363-1 1-139-22020-9 1-139-03190-2 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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
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 recursion and for-loops; 2.5.1. Primitive recursive functions.; 2.5.2. Loop-programs. 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 recursive ordinals. |
| Record Nr. | UNINA-9910827294203321 |
Schwichtenberg Helmut <1942->
|
||
| Cambridge, : Cambridge University Press, 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Proofs and computations / / Helmut Schwichtenberg, Stanley S. Wainer [[electronic resource]]
| Proofs and computations / / Helmut Schwichtenberg, Stanley S. Wainer [[electronic resource]] |
| Autore | Schwichtenberg Helmut <1942-> |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2012 |
| Descrizione fisica | 1 online resource (xiii, 465 pages) : digital, PDF file(s) |
| Disciplina | 511.352 |
| Collana | Perspectives in logic |
| Soggetto topico |
Computable functions
Proof theory |
| ISBN |
1-107-22428-4
1-280-48485-3 1-139-22192-2 9786613579836 1-139-21710-0 1-139-21403-9 1-139-22363-1 1-139-22020-9 1-139-03190-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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
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 recursion and for-loops; 2.5.1. Primitive recursive functions.; 2.5.2. Loop-programs. 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 recursive ordinals. |
| Altri titoli varianti | Proofs & Computations |
| Record Nr. | UNINA-9910461496003321 |
|
Schwichtenberg Helmut <1942->
|
||
| Cambridge : , : Cambridge University Press, , 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Proofs and computations / / Helmut Schwichtenberg, Stanley S. Wainer [[electronic resource]]
| Proofs and computations / / Helmut Schwichtenberg, Stanley S. Wainer [[electronic resource]] |
| Autore | Schwichtenberg Helmut <1942-> |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2012 |
| Descrizione fisica | 1 online resource (xiii, 465 pages) : digital, PDF file(s) |
| Disciplina | 511.352 |
| Collana | Perspectives in logic |
| Soggetto topico |
Computable functions
Proof theory |
| ISBN |
1-107-22428-4
1-280-48485-3 1-139-22192-2 9786613579836 1-139-21710-0 1-139-21403-9 1-139-22363-1 1-139-22020-9 1-139-03190-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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
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 recursion and for-loops; 2.5.1. Primitive recursive functions.; 2.5.2. Loop-programs. 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 recursive ordinals. |
| Altri titoli varianti | Proofs & Computations |
| Record Nr. | UNINA-9910790463503321 |
|
Schwichtenberg Helmut <1942->
|
||
| Cambridge : , : Cambridge University Press, , 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||