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Topic: Interpreting ZFC: Corrected.
Replies: 1   Last Post: May 1, 2013 1:23 PM

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Posts: 2,665
Registered: 6/29/07
Re: Interpreting ZFC: Corrected.
Posted: May 1, 2013 1:23 PM
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On May 1, 12:50 pm, Zuhair <> 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,

> [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 sub-theory 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

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