Author | Malitz, Jerome. author |
---|---|
Title | Introduction to Mathematical Logic [electronic resource] : Set Theory Computable Functions Model Theory / by Jerome Malitz |
Imprint | New York, NY : Springer US, 1979 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-9441-9 |
Descript | XII, 198 p. online resource |
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 โLeast Operatorโ -- 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 Herbrandโs Theorem -- 3.12 Axiomatizing the Validities of L -- 3.13 Some Recent Trends in Model Theory