Appendix 2: The Axiom of Choice In this appendix we want to prove Theorem 1.5. Theorem 1.5. The following set theoretic axioms are equivalentAxiom of Choice) If X is a nonempty set, then there is a map φ : P(X)

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The axiom of choice How (not) to choose innitely many socks Regula Krapf University of Bonn April 27, 2016

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arXiv:1602.07940v2 [physics.data-an] 6 MayThe scaling of the minimum sum of edge lengths in uniformly random trees Juan Luis Esteban1 , Ramon Ferrer-i-Cancho2 and Carlos G´

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• Graph theory
• NP-complete problems
• Spanning tree
• Axiom of choice
• Graph coloring
• Tree

Downloadedto. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php SIAM J. COMPUT. Vol. 2, No. 4, DecemberSET MERGING ALGORITHMS*

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• Graph theory
• Mathematics
• Spanning tree
• Axiom of choice
• Tree
• Minimum spanning tree
• Ear decomposition
• Graph connectivity
• NP-complete problems
• Biconnected component
• Vertex cover

Introduction Open games Determinacy and the Axiom of Choice Axiom of Determinacy The Perfect Subset Property

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• Determinacy
• Axioms of set theory
• Descriptive set theory
• Axiom of determinacy
• Axiom of choice
• L
• Borel determinacy theorem
• Wadge hierarchy

Quantum theory Constructive algebra and geometric mathematics Bas Spitters VALS - LRI, Paris-Sud

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• Constructivism
• Structure
• Mathematics
• Type theory
• Logic
• Constructive proof
• Axiom of choice
• Topos
• Mathematical logic
• Model theory
• Topology

Game characterizations of function classes and Weihrauch degrees MSc Thesis (Afstudeerscriptie) written by Hugo de Holanda Cunha Nobrega (born September 5, 1987 in Petrópolis, Brazil)

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• Mathematical logic
• Mathematics
• Set theory
• Descriptive set theory
• Wadge hierarchy
• Determinacy
• Axiom of countable choice
• Ordinal numbers
• -consistent theory
• Ordinal arithmetic

Power Kripke-Platek set theory and the axiom of choice Michael Rathjen Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, England, Abstract

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I NTRODUCTION P RINCIPLES ADMITTING A UNIVERSAL INSTANCE P RINCIPLES ADMITTING NO UNIVERSAL INSTANCE

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• Computability theory
• Mathematical logic
• Proof theory
• Reverse mathematics
• Model theory
• Axiom of choice

THREE DAYS OF Ω-LOGIC PAUL B. LARSON The Zermelo-Fraenkel axioms for set theory with the Axiom of Choice (ZFC) form the most commonly accepted foundations for mathematical practice, yet it is well-known that many mathe

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