Theory of Sets

Start reading → Description of formal mathematics

1. Front matter
   1. Introduction
   2. To the reader
2. IDescription of formal mathematics
   1. Description of formal mathematics
   2. § 1. Terms and relations5
   3. § 2. Theorems1
   4. § 3. Logical theories
   5. § 4. Quantified theories
   6. § 5. Equalitarian theories3
   7. App. 0. Characterization of terms and relations7
3. IITheory of sets
   1. Theory of sets
   2. § 1. Collectivizing relations10
   3. § 2. Ordered pairs4
   4. § 3. Correspondences37
   5. § 4. Union and intersection of a family of sets22
   6. § 5. Product of a family of sets24
   7. § 6. Equivalence relations13
4. IIIOrdered sets, cardinals, integers
   1. Ordered sets, cardinals, integers
   2. § 1. Order relations. Ordered sets52
   3. § 2. Well-ordered sets28
   4. § 3. Equipotent sets. Cardinals37
   5. § 4. Natural integers. Finite sets15
   6. § 5. Properties of integers30
   7. § 6. Infinite sets26
   8. § 7. Inverse limits and direct limits34
   9. Historical Note
5. IVStructures
   1. Structures
   2. § 1. Structures and isomorphisms17
   3. § 2. Morphisms and derived structures12
   4. § 3. Universal mappings
   5. Historical Note
6. ERSummary of results
   1. § 1. Elements and subsets of a set
   2. § 2. Functions
   3. § 3. Products of sets
   4. § 4. Union, intersection, product of a family of sets
   5. § 5. Equivalence relations and quotient sets
   6. § 6. Ordered sets
   7. § 7. Powers. Countable sets
   8. § 8. Scales of sets. Structures
7. Indexes
   1. Index of notation
   2. Index of terminology