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Full Idea
The Axiom of Reducibility ...had the effect of making impredicative definitions possible.
Clarification
Impredicative definitions introduce nothing new
Gist of Idea
The Axiom of Reducibility made impredicative definitions possible
Source
A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)
Book Ref
George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.47
14459 | Reducibility: a family of functions is equivalent to a single type of function [Russell] |
21720 | Russell saw Reducibility as legitimate for reducing classes to logic [Linsky,B on Russell/Whitehead] |
18130 | Axiom of Reducibility: there is always a function of the lowest possible order in a given level [Russell, by Bostock] |
13428 | Reducibility: to every non-elementary function there is an equivalent elementary function [Ramsey] |
21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
18170 | The Axiom of Reducibility is self-effacing: if true, it isn't needed [Quine] |
21717 | Reducibility undermines type ramification, and is committed to the existence of functions [Quine, by Linsky,B] |
18169 | Axiom of Reducibility: propositional functions are extensionally predicative [Maddy] |
21705 | Reducibility says any impredicative function has an appropriate predicative replacement [Linsky,B] |
17900 | The Axiom of Reducibility made impredicative definitions possible [George/Velleman] |