Axiom of Choice

• Κύριος συγγραφέας: Herrlich, Horst (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
• Σειρά: Lecture Notes in Mathematics, 1876
• Θέματα: Mathematics.; Algebra.; Functional analysis.; Game theory.; Mathematical logic.; Topology.; Combinatorics.; Mathematical Logic and Foundations.; General Algebraic Systems.; Functional Analysis.; Game Theory, Economics, Social and Behav. Sciences.

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...

Πίνακας περιεχομένων:

• 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).