A first course in mathematical logic and set theory
| Main Author: | |
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| Format: | eBook |
| Language: | English |
| Published: |
Hoboken, New Jersey
John Wiley & Sons
2016
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| Subjects: | |
| Online Access: | |
| Collection: | O'Reilly - Collection details see MPG.ReNa |
Table of Contents:
- Includes bibliographical references and index
- Cover
- Title Page
- Copyright
- Dedication
- Contents
- Preface
- Acknowledgments
- List of Symbols
- Chapter 1 Propositional Logic
- 1.1 Symbolic Logic
- 1.2 Inference
- 1.3 Replacement
- 1.4 Proof Methods
- 1.5 The Three Properties
- Chapter 2 First-Order Logic
- 2.1 Languages
- 2.2 Substitution
- 2.3 Syntactics
- 2.4 Proof Methods
- Chapter 3 Set Theory
- 3.1 Sets and Elements
- 3.2 Set Operations
- 3.3 Sets within Sets
- 3.4 Families of Sets
- Chapter 4 Relations and Functions
- 4.1 Relations
- 4.2 Equivalence Relations
- 4.3 Partial Orders
- 4.4 Functions
- 4.5 Injections and Surjections
- 4.6 Images and Inverse Images
- Chapter 5 Axiomatic Set Theory
- 5.1 Axioms
- 5.2 Natural Numbers
- 5.3 Integers and Rational Numbers
- 5.4 Mathematical Induction
- 5.5 Strong Induction
- 5.6 Real Numbers
- Chapter 6 Ordinals and Cardinals
- 6.1 Ordinal Numbers
- 6.2 Equinumerosity
- 6.3 Cardinal Numbers
- 6.4 Arithmetic
- 6.5 Large Cardinals
- Chapter 7 Models
- 7.1 First-Order Semantics
- 7.2 Substructures
- 7.3 Homomorphisms
- 7.4 The Three Properties Revisited
- 7.5 Models of Different Cardinalities
- Index
- EULA.