From Newsgroup: sci.logic
On 09/28/2026 11:22 AM, Ross Finlayson wrote:
On 04/14/2015 01:16 PM, Zuhair wrote:
The following theory is just a minor modification of H.Friedman's
approach to a theory related to Ackerman set theory that can interpret
ZFC. It shows that all axioms of ZFC can be interpreted in a theory
with relatively simply written axiom schemes.
Language: FOL(e,W)
e represent membership
W is a constant symbol
Axioms:
[1] Inclusive Separation: if phi is a formula in which x is not free,
then all closures of
Ak Ex: [Ay(yex<->yek^phi) ^ (keW ->xeW)]
are axioms.
[2] Witnessing: If phi is a formula in the language of FOL(e) having
x1,...,xn,y as its free variables, then all closures of
x1 e W ^..^ xn e W -> [(Ey.phi) -> (EyeW. phi)]
are axioms.
/ Theory definition finished.
This is a usual account showing that class-comprehension vis-a-vis set-comprehension makes any set-theory always formally making models
of the illative and besides as of the extra-ordinary.
Or, Russell can stay in his paradise, others can come and go as
they please, and for tossing things over the fence/wall.
Felix culpa
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