Introduction to Mathematical Logic: Set Theory Computable Functions Model Theory

I: An Introduction to Set Theory.- 1.1 Introduction.- 1.2 Sets.- 1.3 Relations and Functions.- 1.4 Pairings.- 1.5 The Power Set.- 1.6 The Cantor-Bernstein Theorem.- 1.7 Algebraic and Transcendental Numbers.- 1.8 Orderings.- 1.9 The Axiom of Choice.- 1.10 Transfinite Numbers.- 1.11 Paradise Lost, Paradox Found (Axioms for Set Theory).- 1.12 Declarations of Independence.- II: An Introduction to Computability Theory.- 2.1 Introduction.- 2.2 Turing Machines.- 2.3 Etemonstrating Computability without an Explicit Description of a Turing Machine.- 2.4 Machines for Composition, Recursion, and the "Least Operator".- 2.5 Of Men and Machines.- 2.6 Non-computable Functions.- 2.7 Universal Machines.- 2.8 Machine Enumerabihty.- 2.9 An Alternate Definition of Computable Function.- 2.10 An Idealized Language.- 2.11 Definabihty in Arithmetic.- 2.12 The Decision Problem for Arithmetic.- 2.13 Axiomatizing Arithmetic.- 2.14 Some Directions in Current Research.- III: An Introduction to Model Theory.- 3.1 Introduction.- 3.2 The First Order Predicate Calculus.- 3.3 Structures.- 3.4 Satisfaction and Truth.- 3.5 Normal Forms.- 3.6 The Compactness Theorem.- 3.7 Proof of the Compactness Theorem.- 3.8 The Lowenheim-Skolem Theorem.- 3.9 The Prefix Problem.- 3.10 Interpolation and Definabihty.- 3.11 Herbrand's Theorem.- 3.12 Axiomatizing the Validities of L.- 3.13 Some Recent Trends in Model Theory.