Published online by Cambridge University Press: 15 January 2014
1 For (GCA), we define the status of a ∈ {xy: ϕ(x, y)} at α in terms of ϕ(a,{xy: ϕ(x, y)}). This is no trouble than the case for (CA).
2 The fixed point for negation is the statement r ∈ r, where r is {x: x ∉ x}, since we have r ∈ r ↔ ¬(r ∈ r). This generalises to any propositional function: we have {x: F(x ∈ x)} ∈ {x: F(x ∈ x)} ↔ F({x: F(x ∈ x)} ∈ {x: F(x ∈ x)}) for any propositional function F.