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Topic: Tim Chow in Forcing for dummies
Replies: 2   Last Post: Nov 8, 2017 1:18 PM

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Alan Smaill

Posts: 1,099
Registered: 1/29/05
Re: Tim Chow in Forcing for dummies
Posted: Nov 8, 2017 12:29 PM
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WM <wolfgang.mueckenheim@hs-augsburg.de> writes:

> Am Mittwoch, 8. November 2017 17:35:11 UTC+1 schrieb Alan Smaill:
>
>

>> 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.

>
> The models have to respect these axioms (among others):
>
> Axiom VII. The domain contains at least a set Z which contains the
> null-set as an element and is such that each of its elements a is
> related to another element of the form {a}, or which with each of its
> elements a contains also the related set {a} as an element.
>
> Axiom IV. Every set T is related to a second set U(T) (the 'power
> set' of T), which contains all subsets of T and only those as
> elements.
>
> Therefore { }, {{ }}, {{{ }}}, ... happen to be sets in every
> model. And all combinations of these sets happen to be sets,


Non sequitur.

Try and prove that in ZF --
you claim it holds in all models; it follows that it has an FOL
proof. Find that proof, and you have inconsistency of ZF.

Try again.
Fail again.

"No proof required": that was his catchphrase.

--
Alan Smaill



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