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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility

[outdated axiom saying functions reduce to basics]

10 ideas
Reducibility: a family of functions is equivalent to a single type of function [Russell]
Russell saw Reducibility as legitimate for reducing classes to logic [Linsky,B on Russell/Whitehead]
Axiom of Reducibility: there is always a function of the lowest possible order in a given level [Russell, by Bostock]
Reducibility: to every non-elementary function there is an equivalent elementary function [Ramsey]
In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B]
The Axiom of Reducibility is self-effacing: if true, it isn't needed [Quine]
Reducibility undermines type ramification, and is committed to the existence of functions [Quine, by Linsky,B]
Axiom of Reducibility: propositional functions are extensionally predicative [Maddy]
Reducibility says any impredicative function has an appropriate predicative replacement [Linsky,B]
The Axiom of Reducibility made impredicative definitions possible [George/Velleman]