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...
Gorde:
| Egile nagusia: | |
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| Formatua: | Livre numérique |
| Hizkuntza: | Anglais |
| Argitaratua: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Edizioa: | 1st ed. 2006. |
| Saila: | Lecture Notes in Mathematics
1876 |
| Gaiak: | |
| Sarrera elektronikoa: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Oharra: |
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 |
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| 020 | |a 9783540342687 | ||
| 041 | 0 | |a eng | |
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| 084 | |a 03Exx. 2000 | ||
| 084 | |a 54-XX. 2000 | ||
| 100 | 1 | |a Herrlich, Horst, |d 1937-2015. | |
| 245 | 1 | 0 | |a Axiom of choice |c Horst Herrlich. |
| 250 | |a 1st ed. 2006. | ||
| 260 | |a Berlin, Heidelberg : |b Springer Berlin Heidelberg. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Lecture Notes in Mathematics |v 1876 |x 1617-9692 | |
| 500 | |a Description d'après consultation du 10 mars 2011 | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Notes bibliogr. Index | ||
| 505 | 1 | |a 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) | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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 ZF to AC or to some weak form of AC). Disasters happen with AC: Many undesirable mathematical monsters are being created (e.g., non measurable sets and undeterminate games). Some beautiful mathematical theorems hold only if AC is replaced by some alternative axiom, contradicting AC (e.g., by AD, the axiom of determinateness). Illuminating examples are drawn from diverse areas of mathematics, particularly from general topology, but also from algebra, order theory, elementary analysis, measure theory, game theory, and graph theory | ||
| 650 | |a Axiome du choix | ||
| 650 | |a Théorie des jeux | ||
| 650 | |a Logique symbolique et mathématique | ||
| 650 | |a Topologie | ||
| 650 | |a Mathématiques | ||
| 650 | |a Analyse combinatoire | ||
| 650 | |a Analyse fonctionnelle | ||
| 650 | |a Algèbre | ||
| 776 | 0 | |0 10343030X |t Axiom of choice |f Horst Herrlich |d 2006 |c Berlin |n Springer |p 1 vol. (XIV-194 p.) |s Lecture notes in mathematics |z 3-540-30989-6 | |
| 856 | 4 | |q PDF |u https://doi.org/10.1007/11601562 |z Accès sur la plateforme de l'éditeur | |
| 856 | 4 | |u https://revue-sommaire.istex.fr/ark:/67375/8Q1-8P9M1SXJ-6 |z Accès sur la plateforme Istex | |
| 856 | 4 | |5 452349901:747899231 |u https://ezproxy.univ-orleans.fr/login?url=https://dx.doi.org/10.1007/11601562 |z Accès Université d'Orléans | |
| 856 | 4 | |5 180339901:750912243 |u https://ezproxy.insa-cvl.fr/login?qurl=https://dx.doi.org/10.1007/11601562 |z Accès INSA CVL | |
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