Theory of Sets

Inhaltsverzeichnis

• I. Description of Formal Mathematics.
• § 1. Terms and relations.
• § 2. Theorems.
• § 3. Logical theories.
• § 4. Quantified theories.
• § 5. Equalitarian theories.
• Appendix. Characterization of terms and relations.
• Exercises for § 1.
• Exercises for § 2.
• Exercises for § 3.
• Exercises for § 4.
• Exercises for § 5.
• Exercises for the Appendix.
• II. Theory of Sets.
• § 1. Collectivizing relations.
• § 2. Ordered pairs.
• § 3. Correspondences.
• § 4. Union and intersection of a family of sets.
• § 5. Product of a family of sets.
• § 6. Equivalence relations.
• Exercises for § 6.
• III. Ordered Sets, Cardinals, Integers.
• § 1. Order relations. Ordered sets.
• § 2. Well-ordered sets.
• § 3. Equipotent sets. Cardinals.
• § 4. Natural integers. Finite sets.
• § 5. Properties of integers.
• § 6. Infinite sets.
• § 7. Inverse limits and direct limits.
• Exercises for § 7.
• Historical Note on § 5.
• IV. Structures.
• § 1. Structures and isomorphisms.
• § 2. Morphisms and derived structures.
• § 3. Universal mappings.
• Historical Note on Chapters I-IV.
• Summary of Results.
• § 1. Elements and subsets of a set.
• § 2. Functions.
• § 3. Products of sets.
• § 4. Union, intersection, product of a family of sets.
• § 5. Equivalence relations and quotient sets.
• § 6. Ordered sets.
• § 7. Powers. Countable sets.
• § 8. Scales of sets. Structures.
• Index of notation.
• Index of terminology.
• Axioms and schemes of the theory of sets.