Re: Implementable Set Theory and Consistency of ZFC

In article <47f95$47318647$82a1e228$30128@xxxxxxxxxxxxxxxx>,
Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> wrote:

Virgil wrote:

In article <b375d$4730551f$82a1e228$9076@xxxxxxxxxxxxxxxx>,
Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> wrote:

Jesse F. Hughes wrote:

I'm sure I don't know what you mean. I thought you meant:

If NOT (|- (Ex)Px) then |- ~(Ex)Px.

Do you mean something else?

Yes, something else. A set _exists_ as soon as I've _created_ it, with
the rules as laid down by the axioms (1-4). Is it so difficult? I don't
see how to express this with your abacedabra. Yet it's _crystal clear_
and I know HOW to do it.

Then existence of particular "sets" is time dependent, with different
"birthdays" for different sets?

In a sense, yes. _First_ you have {} = 0 . _Second_ you have {0} = 1 .
Thus there is a _temporal order_ in creating those constructable sets.
{{}} = {0} = 1 can not exist before {} = 0 exists.

In normal set theories, set existence is not time dependent, though
proofs of existence are.

Han de Bruijn

Then you should date stamp them.
.

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