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

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Zaljohar@gmail.com

Posts: 2,665
Registered: 6/29/07
Interpreting ZFC: Corrected.
Posted: May 1, 2013 5:50 AM
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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, 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 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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