Theory of Sets
| Main Author: | |
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2004, 2004
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| Edition: | 1st ed. 2004 |
| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 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