Axiom of choice
AC, the axiom of choice, because of its non-constructive character, is the most controversial mathematical axiom, shunned by some, used indiscriminately by others. This treatise shows paradigmatically that: Disasters happen without AC: Many fundamental mathematical results fail (being equivalent in...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Livre numérique |
| Sprache: | Anglais |
| Veröffentlicht: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Ausgabe: | 1st ed. 2006. |
| Schriftenreihe: | Lecture Notes in Mathematics
1876 |
| Schlagworte: | |
| Online Zugang: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Anmerkung: |
Description d'après consultation du 10 mars 2011 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Axiom of choice, Horst Herrlich, 2006, Berlin, Springer, 1 vol. (XIV-194 p.), Lecture notes in mathematics, 3-540-30989-6 |
Inhaltsangabe:
- Origins: Hilbert's First Problem Choice Principles: Some Equivalents to the Axiom of Choice, Some Concepts Related to the Axiom of Choice Elementary Observations: Hidden Choice, Unnecessary Choice, Concepts Split Up: Compactness Disasters without Choice: Finiteness, Disasters in Cardinal Arithmetic, Disasters in Order Theory, Disasters in Algebra I: Vector Spaces, Disasters in Algebra II: Categories, Disasters in Elementary Analysis: The Reals and Continuity, Disasters in Topology I: Countable Sums, Disasters in Topology II: Products (The Tychonoff and the Cech-Stone Theorem), Disasters in Topology III: Function Spaces (The Ascoli Theorem), Disasters in Topology IV: The Baire Category Theorem, Disasters in Graph Theory: Coloring Problems Disasters with Choice: Disasters in Elementary Analysis, Disasters in Geometry: Paradoxical Decompositions Disasters either way: Disasters in Game Theory Beauty without Choice: Lindelöf = Compact, Measurability (The Axiom of Determinateness)