Re: Can ZFC talk about its own models?

On Mar 19, 7:19 pm, "Ross A. Finlayson" <r...@xxxxxxxxxxxxxxx> wrote:
mordov wrote:
Can ZFC talk about its own models? I suspect the answer, maybe not the
whole one, is "Yes". My guess is based on the fact that in ZFC one can
code up a lot of stuff, including structures, formulas, etc. and
define satisfaction predicates and the like. Would anybody be willing
to spell out the answer in greater detail for the good of humanity?

I guess that depends on how closely you read Paul Cohen's paper on
independence of CH, which is where some of the notions of model theory
in terms of ZF arise. He exacts a strict ordering then breaks it.

A strict ordering of what...models? Ordered according to the relation
of elementary extension? I haven't read Paul's paper, but we are on a
first-name basis.

That is to say, part of the answer is "no".

I was hoping there would be more to the answer.

Of course, there are some experts who would share their opinions on
this matter.

I hope so, but I am not fond of subjunctives.

Thanks.

.