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A first course in logic : an introduction to model theory, proof theory, computability, and complexity /
Based on the author's teaching notes, this comprehensive text covers the basics of classical logic, including propositional logic, first-order logic, and second-order logic, as well as proof theory, computability theory, and model theory. Extremely clear, thorough and accurate, this text is ide...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Oxford ; New York :
Oxford University Press,
2004.
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| Colección: | Oxford texts in logic ;
1. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Intro; Contents; 1 Propositional logic; 1.1 What is propositional logic?; 1.2 Validity, satisfiability, and contradiction; 1.3 Consequence and equivalence; 1.4 Formal proofs; 1.5 Proof by induction; 1.5.1 Mathematical induction; 1.5.2 Induction on the complexity of formulas; 1.6 Normal forms; 1.7 Horn formulas; 1.8 Resolution; 1.8.1 Clauses; 1.8.2 Resolvents; 1.8.3 Completeness of resolution; 1.9 Completeness and compactness; 2 Structures and first-order logic; 2.1 The language of first-order logic; 2.2 The syntax of first-order logic; 2.3 Semantics and structures; 2.4 Examples of structures
- 2.4.1 Graphs2.4.2 Relational databases; 2.4.3 Linear orders; 2.4.4 Number systems; 2.5 The size of a structure; 2.6 Relations between structures; 2.6.1 Embeddings; 2.6.2 Substructures; 2.6.3 Diagrams; 2.7 Theories and models; 3 Proof theory; 3.1 Formal proofs; 3.2 Normal forms; 3.2.1 Conjunctive prenex normal form; 3.2.2 Skolem normal form; 3.3 Herbrand theory; 3.3.1 Herbrand structures; 3.3.2 Dealing with equality; 3.3.3 The Herbrand method; 3.4 Resolution for first-order logic; 3.4.1 Unification; 3.4.2 Resolution; 3.5 SLD-resolution; 3.6 Prolog; 4 Properties of first-order logic
- 4.1 The countable case4.2 Cardinal knowledge; 4.2.1 Ordinal numbers; 4.2.2 Cardinal arithmetic; 4.2.3 Continuum hypotheses; 4.3 Four theorems of first-order logic; 4.4 Amalgamation of structures; 4.5 Preservation of formulas; 4.5.1 Supermodels and submodels; 4.5.2 Unions of chains; 4.6 Amalgamation of vocabularies; 4.7 The expressive power of first-order logic; 5 First-order theories; 5.1 Completeness and decidability; 5.2 Categoricity; 5.3 Countably categorical theories; 5.3.1 Dense linear orders; 5.3.2 Ryll-Nardzewski et al.; 5.4 The Random graph and 0-1 laws; 5.5 Quantifier elimination
- 5.5.1 Finite relational vocabularies5.5.2 The general case; 5.6 Model-completeness; 5.7 Minimal theories; 5.8 Fields and vector spaces; 5.9 Some algebraic geometry; 6 Models of countable theories; 6.1 Types; 6.2 Isolated types; 6.3 Small models of small theories; 6.3.1 Atomic models; 6.3.2 Homogeneity; 6.3.3 Prime models; 6.4 Big models of small theories; 6.4.1 Countable saturated models; 6.4.2 Monster models; 6.5 Theories with many types; 6.6 The number of nonisomorphic models; 6.7 A touch of stability; 7 Computability and complexity; 7.1 Computable functions and Church's thesis
- 7.1.1 Primitive recursive functions7.1.2 The Ackermann function; 7.1.3 Recursive functions; 7.2 Computable sets and relations; 7.3 Computing machines; 7.4 Codes; 7.5 Semi-decidable decision problems; 7.6 Undecidable decision problems; 7.6.1 Nonrecursive sets; 7.6.2 The arithmetic hierarchy; 7.7 Decidable decision problems; 7.7.1 Examples; 7.7.2 Time and space; 7.7.3 Nondeterministic polynomial-time; 7.8 NP-completeness; 8 The incompleteness theorems; 8.1 Axioms for first-order number theory; 8.2 The expressive power of first-order number theory; 8.3 Gödel's First Incompleteness theorem