Prev: Models of set theory vs. models of first order theories
Next: Cantor's Diagonal?
From: Jan Burse on 5 Feb 2010 12:37
MoeBlee schrieb:
> On Feb 5, 10:26 am, Jan Burse <janbu...(a)fastmail.fm> wrote:
>
>> There are papers on the net(*) that show that transfinite recursion
>> is part of ZFC.
>
> What do you mean by "part of ZFC"?
derivable

>> So it seems that weaker systems only make
>> a difference. Right?
>
> I don't understand your question. What difference are you referring
> to?
not derivable
> MoeBlee
>
From: MoeBlee on 5 Feb 2010 12:54
On Feb 5, 11:37 am, Jan Burse <janbu...(a)fastmail.fm> wrote:
> MoeBlee schrieb:> On Feb 5, 10:26 am, Jan Burse <janbu...(a)fastmail.fm> wrote:
>
> >> There are papers on the net(*) that show that transfinite recursion
> >> is part of ZFC.
>
> > What do you mean by "part of ZFC"?
>
> derivable

Of course the main transfinite recursion schemata are derviable in ZF.
And, as far as I know, certain of the transfinite recursion schemata
are not derivable in Z.

But what about it?

MoeBlee

From: Jan Burse on 5 Feb 2010 14:14
MoeBlee wrote:
> On Feb 5, 11:37 am, Jan Burse <janbu...(a)fastmail.fm> wrote:
>> MoeBlee schrieb:> On Feb 5, 10:26 am, Jan Burse <janbu...(a)fastmail.fm> wrote:
>>
>>>> There are papers on the net(*) that show that transfinite recursion
>>>> is part of ZFC.
>>> What do you mean by "part of ZFC"?
>> derivable
>
> Of course the main transfinite recursion schemata are derviable in ZF.
> And, as far as I know, certain of the transfinite recursion schemata
> are not derivable in Z.
>
> But what about it?
>
> MoeBlee
>
The set theoretic content is the delta from the theory X where
it is not derivable, to the theory X+Y where it is derivable.
In the simple case Y is just some axiom that expresses transfinite
recursion more or less literally.

But by the article from Wolf, I was only glossing, it seems to
me that there are other meaningful interactions and possibilities
for X and X+Y. With even less tight boundaries.

Bye
From: Bill Taylor on 5 Feb 2010 23:10
I would just like to applaud this wonderful piece of sarcasm about
Ross Finlayson, by MoeBlee <jazzm...(a)hotmail.com> who answered

> > In set theoretic structures these generally use ordinals. With
> > cardinals there would still be maintained the space. Yet, that is
> > where the measurement in keeping the variables transparent to
> > cardinals would expand the regular space, adjusting the refinement.
> > Ordinals, maintain cross-discretely, they're ordinal-valued. The
> > refinement, here that addresses when maintaining the cardinals in the
> > set theoretic framework reduces to ordinals through refinement.
> > Seriously, this makes sense to me, the space that the cardinals
> > maintain is where the functions of inter-related variables are scaled
> > together so they're analyzed together, maintaining analog function spaces.

I imagine most serious posters here will agree that the above is
incomprehensible egregious nonsense, and similarly appreciate...

> Some of your finest nonsense. I especially admire the way you build,
> getting yet more and more outlandishly ridiculous with each sentence.

Wonderful! I also can't understand a sentence of the above excerpt,
indeed it is, as they say, "not even wrong".

The only place where I understand and agree with it,
is where the author says:

"Seriously, this makes sense to me,"

I'm sure it does, and also that he is the only one to whom it makes
any kind of sense. Thanks Moe!

-- Bewildered Bill

** What an intellectual! - the Sorbonne, Magdalen College Oxford,
** King's College Cambridge, Imperial College London, UCLA,
** Trinity College Dublin, Harvard, MIT - he's heard of them all!
From: MoeBlee on 9 Feb 2010 10:30
On Feb 5, 10:09 am, MoeBlee <jazzm...(a)hotmail.com> wrote:

> If I do show that the theorem
> unpacks to a definition of a set of ZF theorems, then not only is the
> "significance" of the theorem justfication of the tactical,
> syntactical tool of adding operation symbols with transfinite
> recursive definitions, but also the actual individual theorems taken
> as a set.

Okay, I did that. I translated Kunen's formulations so that they
amount to a single axiom schema that defines an infinite set of
theorems of ZF. So the conclusion stated in the quote above is good.

MoeBlee

First  |  Prev  |  Next  |  Last
Pages: 1 2 3 4 5
Prev: Models of set theory vs. models of first order theories
Next: Cantor's Diagonal?