FOM: Re:The missing 1%

Hasan Keler nx at
Sun Feb 20 04:25:14 EST 2000

I asked:

>   "ZFC is a foundation of the 99% of mathematics."
>But what is the remaining 1% ?
>And why is ZFC not a foundation of this 1% ?

Edwin Mares wrote:

>I should think that category theory is the remainder.

To be honest, I don't know much category theory. Are categories proper
classes in general rather than sets? Is this your reason why you don't
consider category theory as something not in the reach of ZFC? What if we
use NBG?

Jeffrey Ketland wrote a a historical survey which was very helpful. At some
point he writes:

>However, it is remains true that 99% of "ordinary" mathematical theorems
>(perhaps 99.9999%) can be translated into the language of set theory and

Also Matt Insall writes:

>Mathematicians ... seem to act as though everything they do
>could, and someday will, be encoded in ZFC.

Naturally, the following question comes to me:

Is there a theorem of "ordinary" mathematics that can NOT be translated into
the language of set theory ?

Note: In my previous posting I forgot to write a subject header. I apologize
for any inconvinience this may have caused.

Hasan Keler
nx at
First year graduate student at
Dept. of Mathematics,
Middle East Technical University,
Ankara, Turkey.

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