[FOM] Uncountable structures and `core mathematics'

[Harvey Friedman]

On 2/19/06 10:27 AM, "John Baldwin" <jbaldwin at uic.edu> wrote:

> Here are some interactions between the study of the `uncountable' and core
> mathematics.
> 
> I have a couple of follow-ups on this that I should post in a few days.
> 

Are these in the category of:

1. various set theoretic notions coming up naturally in the model theoretic
treatment of core mathematics turn out to be equivalent to natural concrete
notions.

2. various set theoretic notions coming up naturally in core mathematics
turn out to be equivalent to natural concrete notions.

3. various set theoretic notions used by core mathematicians turn out to be
equivalent to natural concrete notions.

rather than 

4. substantial set theoretic methods (countable but highly impredicative)
are used by core mathematicians in treating countable objects.

I notice that you rather carefully used the word "some interactions".

Harvey