Re: Implementable Set Theory and Consistency of ZFC

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

Jesse F. Hughes wrote:

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

Jesse F. Hughes wrote:

But whatever it means, since a model of ZFC is also a model of
ZFC - Infinity, you seem to be claiming that you can build an infinite
set using only the first four axioms.

But the reverse is not true: a model of (ZFC - Infinity) is not a model
of ZFC(Infinity included). So I'm building only (ZFC - Infinity), with
those first four axioms: extensionality, empty set, pairing, union. All
finite sets can be build with these 4 axioms (but there are infinitely
many of these finite sets, like with the naturals).
In other words, you are *not* speaking about every model of ZFC -
Infinity, despite what you claimed.
And just as I suggested.

Have no idea what you are talking about, with your "every model".

Look, here's what you said:

It's not clear to me what the last claim means, but regardless, it
must mean something about "all sets" in this particular model of
ZFC - Infinity and not all sets of ZFC.

No. It's about all sets in (ZFC - Infinity). And the "particular
model"
is any implementation, is anything applicable.

Why not just tell me what you meant when you said that your claim
applied to "any implementation" if not "any model of these eight
axioms"?

--
"So how do you go on? [...] How will you keep moving for the next few
weeks or months until you are known for what you are, the story
becomes huge all over the world, and you have reporters at your
schools asking you, why?" -- Another JSH mystery
.

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