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.