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## Mathematical Logic A Course With Exercises, Part II Recursion theory, Godel's theorems, set theory, model theory

Language: English Publication details: Oxford Oxford University Press 2001Description: xx, 331 pISBN: 9780198500506 (PB)Subject(s): Logic, Symbolic and mathematical | Mathematics
Contents:
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
Summary: The requirement to reason logically forms the basis of all mathematics, and hence mathematical logic is one of the most fundamental topics that students will study. Assuming no prior knowledge of the topic, this book provides an accessible introduction for advanced undergraduate students.
Item type: BOOKS List(s) this item appears in: New Arrivals (30 May 2023)
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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

The requirement to reason logically forms the basis of all mathematics, and hence mathematical logic is one of the most fundamental topics that students will study. Assuming no prior knowledge of the topic, this book provides an accessible introduction for advanced undergraduate students.

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