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...
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Format: | eBook |
Language: | English |
Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2006, 2006
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Edition: | 1st ed. 2006 |
Series: | Lecture Notes in Mathematics
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Subjects: | |
Online Access: | |
Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- 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)