Re: a question
- From: Gc <Gcut667@xxxxxxxxxxx>
- Date: Thu, 27 Dec 2007 06:13:10 -0800 (PST)
On 27 joulu, 15:08, David C. Ullrich <ullr...@xxxxxxxxxxxxxxxx> wrote:
On Wed, 26 Dec 2007 09:10:43 -0800 (PST), Gc <Gcut...@xxxxxxxxxxx>
wrote:
On 26 joulu, 16:46, David C. Ullrich <ullr...@xxxxxxxxxxxxxxxx> wrote:
On Wed, 26 Dec 2007 02:05:08 -0800 (PST), Gc <Gcut...@xxxxxxxxxxx>
wrote:
Let`s suppose a non-recursive extension of the Robinson arithmetic
"proves" every true arithmetical statement. Is this theory necessarily
complete?
OBviously, for the same reason that the theory of _any_ structure
is complete: For any P, either P is true in that structure
or ~P is.
Regarding that, note that of course I was assuming that the
theory is in the same language. (Thanks, Aatu.)
I meant by a extension of the robinson arithemetic any theory which
can prove everything that the Robinson arithemetic can,
Yes, that's what "extension" means.
Not exactly. You can read what an "extension" means in any standard
textbook of logic.
so expecially
ZFC suffices.
ZFC suffices to prove every true arithmetical statement? Wow,
that's big news. Really big.
Huoh.
.
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