Date: Apr 6, 2013 11:03 AM
Author: namducnguyen
Subject: Re: Matheology § 224

On 06/04/2013 8:35 AM, WM wrote:
> On 6 Apr., 16:13, Nam Nguyen <namducngu...@shaw.ca> wrote:
>> On 06/04/2013 7:32 AM, Peter Percival wrote:
>>

>>> Nam Nguyen wrote:
>>
>>>> But if GC is undecidable in PA, there's no proof left in FOL but
>>>> _structure theoretically verifying_ the truth value of GC in
>>>> this structure.

>>
>>> If the Goldbach conjecture is undecidable in PA then it is true.
>>
>> Care to verify (prove) your claim here?

>
> Goldbach conjecture is false. <==> Counter example exists. <==>
> Counter example can be found. <==> Goldbach conjecture is decidable.
>
> The second equivalence requires to neglect reality. But in mathematics
> this is standard.


But, to start with, how would one _structure theoretically prove_ the
1st equivalence:

"Goldbach conjecture is false. <==> Counter example exists."

?

Logically:

(A _specific_ counter example exists) => (Goldbach conjecture is false).

How would one _prove_ ( i.e. _structure theoretically verify_ ) the
other-way-around?

Consider:

(P(0) -> Ex[P(x)]) <-> (Ex[P(x)] -> P(0))

Is this a logical equivalence?

--
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There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI
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