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Topic: How simple Z is?
Replies: 1   Last Post: Apr 23, 2013 11:10 PM

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Graham Cooper

Posts: 4,320
Registered: 5/20/10
Re: How simple Z is?
Posted: Apr 23, 2013 11:10 PM
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On Apr 24, 5:23 am, Zuhair <zaljo...@gmail.com> wrote:
> Pre-Z is the closure of all of what is provable from the logical
> axioms of first order logic and the following axioms by the rules of
> inference of first order logic (Hilbert style).
>
> Comprehension: if phi is a formula then a set {x C A| phi} exists.
>




Yes.

ZFC Comprehension

A(Z) E(Y) A(X) XeY <-> XeZ & phi

NST

E(Y) A(X) XeY <-> phi

-----------------------------


ZFC breaks the above biconditional.

ZFC

E(Y) A(X) XeY -> phi



-----------------------------


Change <-> to ->
and you go from NST to ZFC.

----------------------------


Better still, use CBL where a WFF is TRUE XOR FALSE
then NST is consistent.


Herc



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