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Full Idea
In the superior realist and simple theory of types, the place of the axiom of reducibility is not taken by the axiom of classes, Zermelo's Aussonderungsaxiom.
Gist of Idea
In simple type theory the axiom of Separation is better than Reducibility
Source
report of Kurt Gödel (Russell's Mathematical Logic [1944], p.140-1) by Bernard Linsky - Russell's Metaphysical Logic 6.1 n3
Book Ref
Linsky,Bernard: 'Russell's Metaphysical Logic' [CSLI 1999], p.91
A Reaction
This is Zermelo's Axiom of Separation, but that too is not an axiom of standard ZFC.
| 10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
| 21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
| 10035 | Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel] |
| 10038 | A logical system needs a syntactical survey of all possible expressions [Gödel] |
| 10039 | Some arithmetical problems require assumptions which transcend arithmetic [Gödel] |
| 10042 | Reference to a totality need not refer to a conjunction of all its elements [Gödel] |
| 10043 | Mathematical objects are as essential as physical objects are for perception [Gödel] |
| 10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |
| 10046 | The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel] |