[FOM] Micro Set Theory

[Andrej Bauer]

On Fri, May 17, 2013 at 6:56 PM, <joeshipman at aol.com> wrote:

> To reiterate -- "answer" is not the same as "understand", I am just asking
> for answers assuming that the oracle is correct. I am looking for a finite
> object such that to understand this object is comparable to understanding
> mathematics in general, noting that V7 appears to be such an object, asking
> if V6 is such an object, and asking if V5 partakes of any of the difficulty
> of "mathematics in general" or whether it is instead "easy to understand".
>
>
It is a bit confusing that you say both "'answer' is not the same as
'understand', I am just asking for answers ..." as well as "I am looking
for and object such that to understand this object is comparable to
understanding mathematics".

In any case, is there anything special about V_7 here? We could take an
"initial segment" of any kind of structure that allows us to perform
coding, and we'd be in the same situation.
V_7 is just a bunch of finite trees. You could take all finite tress of
given size. Or take a large number N and consider the initial segment
[0..N], as a structure with + and *, where you do something reasonable to
indicate overflow. Anyone who can answer questions about this structure,
presumably has to have a pretty good understanding about mathematics.

And even if you take something like all finite groups up to size N, then
anyone who can answer questions about such groups must be pretty
knowledgable about all finite groups. Has this sort of phenomenon been
quantified and studied in model theory?

Andrej Bauer
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