Mathematical Logic: Part 2

"An undergraduate course text for students who have acquired the practice and knowledge of classical mathematics as taught in high school and the first year of college, but no specialized knowledge. Introducing the logic underlying mathematics and theoretical computer science, Cori and Lascar (both U. Paris VII) use the concept of model as their underlying theme. Pelletier (York U. Toronto) has clarified some of the terminology in English for beginning students."--SciTech Book News<br> "I have always been especially fond of logic. The two-volume Mathematical Logic: A Course with Exercises is a comprehensive introductory course that is distinguished by clarity of exposition and a large number of exercises with thorough solutions. Each volume is about 330 pages long, 80 of which are solutions!"The Bulletin of Mathematics Books<br>

Contents of Part I; Notes from the translator; Notes to the reader; 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