The requirement to reason logically forms the basis of all mathematics, and hence mathematical logic is one of the most fundamental topics that students study. Assuming no prior knowledge of the topic, this book provides an introduction for advanced undergraduate students. The concept of model underlies the text, giving it a theoretical coherence.
The requirement to reason logically forms the basis of all mathematics, and hence mathematical logic is one of the most fundamental topics that students study. Assuming no prior knowledge of the topic, this book provides an introduction for advanced undergraduate students. The concept of model underlies the text, giving it a theoretical coherence.
Introduction 5: Recursion theory 5.1: Primitive recursive functions and sets 5.2: Recursive functions 5.3: Turing machines 5.4: Recursively enumerable sets 5.5: Exercises for Chapter 5 6: Formalization of arithmetic, Godel's theorems 6.1: Peano's axioms 6.2: Representable functions 6.3: Arithmetization of syntax 6.4: Incompleteness and undecidability theorem 7: Set theory 7.1: The theories Z and ZF 7.2: Ordinal numbers and integers 7.3: Inductive proofs and definitions 7.4: Cardinality 7.5: The axiom of foundation and the reflections schemes 7.6: Exercises for Chapter 7 8: Some model theory 8.1: Elementary substructures and extensions 8.2: Construction of elementary extensions 8.3: The interpolation and definability theorems 8.4: Reduced products and ultraproducts 8.5: Preservations theorems 8.6: -categorical theories 8.7: Exercises for Chapter 8 Solutions to the exercises of Part II Chapter 5 Chapter 6 Chapter 7 Chapter 8 Bibliography Index
Introduction 5: Recursion theory 5.1: Primitive recursive functions and sets 5.2: Recursive functions 5.3: Turing machines 5.4: Recursively enumerable sets 5.5: Exercises for Chapter 5 6: Formalization of arithmetic, Godel's theorems 6.1: Peano's axioms 6.2: Representable functions 6.3: Arithmetization of syntax 6.4: Incompleteness and undecidability theorem 7: Set theory 7.1: The theories Z and ZF 7.2: Ordinal numbers and integers 7.3: Inductive proofs and definitions 7.4: Cardinality 7.5: The axiom of foundation and the reflections schemes 7.6: Exercises for Chapter 7 8: Some model theory 8.1: Elementary substructures and extensions 8.2: Construction of elementary extensions 8.3: The interpolation and definability theorems 8.4: Reduced products and ultraproducts 8.5: Preservations theorems 8.6: -categorical theories 8.7: Exercises for Chapter 8 Solutions to the exercises of Part II Chapter 5 Chapter 6 Chapter 7 Chapter 8 Bibliography Index
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