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Axiom of Choice in Weak Set Theories by jeremyjager is a document available to read on EtoBox.

What is Axiom of Choice in Weak Set Theories about?

This document discusses how the axiom of choice (AC) and the law of excluded middle (LEM) relate in weak set theories. It shows that: 1) In intuitionistic set theory, AC entails LEM, but in type theories AC is derivable and does not entail LEM. 2) For AC to derive LEM, sets need a degree of extensionality or the ability to form quotient sets. 3) The document defines a weak set theory WST and examines adding various extensionality principles or the axiom of quotients to see which allow deriving LEM from

Author

jeremyjager

Language

EN