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Dedication
by Michael L. O'Leary
A First Course in Mathematical Logic and Set Theory
Cover Page
Title Page
Copyright
Dedication
CONTENTS
PREFACE
ACKNOWLEDGMENTS
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
APPENDIX: ALPHABETS
REFERENCES
INDEX
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