Theory of Sets

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 § 1.- Exercises for § 2.- Exercises for § 3.- Exercises for § 4.- Exercises for § 5.- 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 § 1.- Exercises for § 2.- Exercises for § 3.- Exercises for § 4.- Exercises for § 5.- Exercises for § 6.- Exercises for § 7.- Historical Note on § 5.- IV. Structures.- § 1. Structures and isomorphisms.- § 2. Morphisms and derived structures.- § 3. Universal mappings.- Exercises for § 1.- Exercises for § 2.- Exercises for § 3.- 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.