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Topic: Tim Chow in Forcing for dummies
Replies: 3   Last Post: Nov 8, 2017 11:54 AM

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 Alan Smaill Posts: 1,103 Registered: 1/29/05
Re: Tim Chow in Forcing for dummies
Posted: Nov 8, 2017 11:33 AM

WM <wolfgang.mueckenheim@hs-augsburg.de> writes:

> Am Mittwoch, 8. November 2017 14:40:07 UTC+1 schrieb Alan Smaill:
>> WM <wolfgang.mueckenheim@hs-augsburg.de> writes:
>>

>> > No. There is no model dependence. First we have to guarantee that
>> > omega is there and simultaneously P(omega) will be there. And then we
>> > can look for a model satisfying that requirement.

>>
>> This is truly miraculous:

>
> No, it is an axiom.

Keep the jokes coming.

> The axiom does not depend on any model.
>
> Axiom IV. Jeder Menge T entspricht eine zweite Menge ?T (die
> "Potenzmenge" von T), welche alle Untermengen von T und nur solche als
> Elemente enthält. [E. Zermelo: "Untersuchungen über die Grundlagen der
> Mengenlehre I", Math. Ann. 65 (1908) p. 265] "Every set T is related
> to a second set ?(T) (the 'power set' of T), which contains all
> subsets of T and only those as elements."

So what?

Of course the axiom does not depend on the model.

But the models simply have to respect the axiom, in that
all the collections *that happen to be sets* and
where every element is in X will be in the power set of X.

More than that is achieved only by Magical Incantation,

>> Who needs proof when we have WM's Infallible Judgement?
>>
>> "No proof is required": that was His catchphrase.

>
> You confuse things. I said "no axioms are required".

You told us that no proof is required to show that the set of even
numbers is a subset of |N. You were certainly unable to provide such a
proof.

"No proof is required": that was his catchphrase.

> Regards, WM

--
Alan Smaill