Re: Skolem Paradox Question

On Apr 11, 12:04 pm, stevendaryl3...@xxxxxxxxx (Daryl McCullough)
wrote:

I don't know why you say it is meaningless.
Let's define "M is standard"
to mean "M is elementarily equivalent
to V_kappa for some inaccessible
cardinal kappa".

This is basically meaningful only if both
standard and nonstandard models can exist.
There are models of ZFC in which inaccessible cardinals
DO NOT exist. In these models, there does not
exist the kappa required, yet all M's are still going to be
elementarily equivalent to whatever they are elementarily
equivalent to. Concerns about the meaninglessness or
inapplicabilit of that definition therefore do remain valid
unless the axiomatic framework is ZFC+IC as ooposed to ZFC.
In particular, suppose the axiomatic framework were
ZFC~IC: how then could this definition be applied?
This is almost like saying that IC must be true in standard
models.


.

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