Definition:Zermelo-Fraenkel-Skolem Set Theory/Historical Note

Historical Note on Zermelo-Fraenkel-Skolem Set Theory
It was who proposed the amendment to Zermelo-Fraenkel set theory to sharpen the specification of the axiom of replacement.

He considered it necessary to express the axiom of subsets as an infinite number of axioms: one for every first order formula.

disagreed forcefully against 's approach, preferring the philosophical position that a property should be allowed to be considered as all possible meaningful conditions, not just propositions in first order logic.

's position was that 's notion of property was too vague to be completely satisfactory.