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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 7, 2012 5:48 PM

On Oct 8, 6:38 am, George Greene <gree...@email.unc.edu> wrote:
>
> Another point that makes enumeration irrelevant is that all the new
> theorems
> that you get from the axioms were in fact already present from the
> UNDERLYING VALIDITIES that were provable FROM NO axioms,
> because every proved theorem only USES a FINITE number of the axioms.
> Thus, if the theorem was "h" and the axioms (or instances of axioms)
> used
> to prove it were a,b,c,d,f, and g, then
> a^b^c^d^f^f->h
> a first-order validity.  So there really is a sense in which the
> axioms merely
> highlight a subset of the validities, as opposed to adding new stuff.
> The order in which this highlighting occurs IS NOT important.
> I'm SORRY FOR YOU, HERC, that the only treatment YOU have seen
> HAPPENS to STRESS the "enumeration".  You're a victim of a lame
> education.
> Which would be easily cured if you only had sense enough to read
> ANOTHER book.

You can stick to "ENUMERABLE" if you are too clueless to WORK_OUT the
ENUMERATION.

ATLEAST THAT'S SOMETHING TANGIBLE!

BUT YOU ARE CONTRADICTING YOURSELF ALL OVER THE PLACE.

YOU SAID THE SET OF TRUTHS ARE 'AUTOMATIC' AND NOT POSSIBLE TO DERIVE
FROM AN ALGORITHM.

Herc
--

GEORGE'S SET THEORY!
*****************************

GEORGE'S RELATION ALGEBRA!
aRb

GEORGE'S INFERENCE RULES!
P -> P
~(X -> ~X)
a^b^c^d^f^g->h

GEORGE'S SET AXIOMS!
1. Extensionality:
AxAy [Az (zex <-> zey) -> x=y]
2. Regularity:
Ax [Ea (aex) <-> Ey (yex & ~Ez (zey & zex))]
3. Specification Schema:
AzAw_1...w_nEyAx [xey <-> (xez & phi)]
4. Pairing:
AxAyEz (xez & yez)
5. Union:
AfEaAyAx [(xey & yef) -> xea]
6. Replacement Schema:
AaAw_1...w_n [Ax (xea -> E!y phi) -> EbAx (xea -> Ey (yeb & phi)]
7. Infinity:
Ex [0ex & Ay (yex -> S(y)ex)]
8. Powerset:
AxEyAz [z subset x -> zey]
9. Wellordering:
AxEr (r wellorders x)

GEORGE'S VALIDATED SENTENCES!
THEOREM 1 = ..
THEOREM 2 = ..
THEOREM 3 = !E(R) XeR <-> !(XeX) *TADAAAA*

Date Subject Author
10/5/12 Graham Cooper
10/5/12 Frederick Williams
10/7/12 Charlie-Boo
10/5/12 Graham Cooper
10/5/12 Frederick Williams
10/5/12 Graham Cooper
10/7/12 Graham Cooper
10/8/12 Graham Cooper
10/9/12 Graham Cooper
10/11/12 Graham Cooper
10/12/12 Graham Cooper
10/12/12 Graham Cooper
10/12/12 camgirls@hush.com
10/12/12 Richard Tobin
10/12/12 camgirls@hush.com
10/13/12 george
10/13/12 Graham Cooper
10/14/12 george
10/13/12 Graham Cooper
10/13/12 george
10/13/12 george
10/13/12 Graham Cooper
10/14/12 Graham Cooper
10/14/12 Graham Cooper
10/14/12 Graham Cooper
10/5/12 Scott Berg
10/5/12 Curt Welch
10/6/12 Mike Terry
10/6/12 Graham Cooper