Re: Implementable Set Theory and Consistency of ZFC

Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> writes:

Jesse F. Hughes wrote:

Here's what I think you *can* say: Statements (5)-(8) are true in your
model and your model is canonical in a sense (I think it's minimal).
It is not the case that (5)-(8) are therefore *entailed* by (1)-(4) in
any sense of the word that I understand.

It seems that I can learn something from you here. Please explain to
me the words "canonical" and "minimal" and what they mean in this
context.

I hesitate to do so, because it has been a long time since I did any
model theory and my claim may be just ***-wrong.

By "canonical" here, I meant nothing more than a model which is
special in some sense and the sense I had in mind was given in
"minimal". It seems to me that your model contains every set required
by axioms (1)-(4) and no sets that are not required and so it is
apparently minimal. If I were to hazard a guess, I would say that
there is a model homomorphism mapping your model into any other model
of (1)-(4). I would further guess that this homomorphism is
one-to-one.

But I could be all wrong on these properties and so one shouldn't take
my word for it.

--
Jesse F. Hughes
"Eventually, I guess, I'll overcome my reticence and fear of failure and
check my own work. But not today."
--James S. Harris, in a moment of honesty
.

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