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Re: Interpreting ZFC: Corrected.
Posted:
May 1, 2013 1:23 PM


On May 1, 12:50 pm, Zuhair <zaljo...@gmail.com> wrote: > I made a mistake in my previous post to this Usenet titled as > Interpreting ZFC. > > The correct formulation must be the following: > > BI is the closure of all sentences entailed by FOL(e) from the > following axioms: > > (1) Boundedness: if phi is a formula
In which B is not free,
then: > > [EB: (Vy in B(Ex C A:phi)) & (Vx C A ((Ey:phi) >(Ey in B:phi)))] > > is an axiom. > > Where C is a modified subset relation defined as: > > x C A iff Vm in x (En: n in A & m in n) > > V,E signifies universal and existential quantification respectively. > > 2) Infinity. > / > > Now clearly BI is a subtheory of ZFC. Yet BI interpret the whole of > ZFC! > > BI depicts a marvelous use of the property of transitivity of sets, BI > interprets ZFC over the realm of the cumulative hierarchy using the > properties of transitive sets which constitutes the stages of that > hierarchy. > > It is a nice experience to try interpret the whole of ZFC inside BI. > > Zuhair



