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Axiom of Choice / by Horst Herrlich.
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View onlineMath/Physics/Astronomy Library QA3 .L28 v.1-999 470,523,830,849:2nd ed. v.1000-1722,1762,1781,1799-2099,2100-2192-2218 2219-2223-2258,2260-2271,2273-2274-2277,2279-2281,2283-2289,2291,2293-2294,2296,2298-2299,2300-2311,2313-2379,2381-2384 2385-2386,2388-2389
Mixed Availability
LIBRA QA3 .L28 Scattered vols.
Mixed Availability
- Format:
- Book
- Author/Creator:
- Herrlich, Horst, author.
- Series:
- Lecture Notes in Mathematics, 0075-8434 ; 1876.
- Lecture Notes in Mathematics, 0075-8434 ; 1876
- Language:
- English
- Subjects (All):
- Logic, Symbolic and mathematical.
- Algebra.
- Functional analysis.
- Mathematics.
- Combinatorial analysis.
- Topology.
- Mathematical Logic and Foundations.
- General Algebraic Systems.
- Functional Analysis.
- Game Theory, Economics, Social and Behav. Sciences.
- Combinatorics.
- Local Subjects:
- Mathematical Logic and Foundations.
- General Algebraic Systems.
- Functional Analysis.
- Game Theory, Economics, Social and Behav. Sciences.
- Combinatorics.
- Topology.
- Physical Description:
- 1 online resource (XIV, 198 pages 1 illustrations).
- Contained In:
- Springer eBooks
- Place of Publication:
- Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
- System Details:
- text file PDF
- Summary:
- 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.
- 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).
- Other Format:
- Printed edition:
- ISBN:
- 9783540342687
- Access Restriction:
- Restricted for use by site license.
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