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Topic: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Replies: 39   Last Post: Oct 14, 2012 11:56 PM

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 Graham Cooper Posts: 4,495 Registered: 5/20/10
Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Posted: Oct 12, 2012 5:49 PM

On Oct 13, 5:40 am, George Greene <gree...@email.unc.edu> wrote:
> > On Oct 12, 2:06 pm, George Greene <gree...@email.unc.edu> wrote:
> > >http://en.wikipedia.org/wiki/First-order_logic
>
> On Oct 12, 3:02 am, Graham Cooper <grahamcoop...@gmail.com> wrote:
>

> > Hilbert-style systems and natural deduction
>
> Why are you bothering to quote a difference between
> Hilbert-systems and natural-deduction-systems?
>
> What difference does THAT make?

deductive system is a list of formulas,
each of which is a logical axiom

there is no decision procedure
that determines whether arbitrary formulas are logically valid

So much for your ALGORITHMIC proof that

~E(r) xer <-> ~xex

is a part of ZFC AUTOMATICALLY.

Herc

Date Subject Author
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