Re: Countable models of ZFC
- From: Rupert <rupertmccallum@xxxxxxxxx>
- Date: Mon, 01 Oct 2007 10:50:02 -0700
On Oct 1, 10:17 pm, george <gree...@xxxxxxxxxx> wrote:
On Sep 28, 7:06 pm, Rupert <rupertmccal...@xxxxxxxxx> wrote:
What I wanted to say
THEN YOU SHOULD HAVE SAID IT,
A LOT sooner, INSTEAD OF SAYING
all this irrelevant junk you were saying
about my attitude.
I thought it would have been clear enough the first time I said it to
anyone who wasn't of subhuman intelligence. I won't have any lectures
from you about what I should do, thank you. Your behaviour leaves a
lot to be desired and my comments about it are not "irrelevant junk".
You ought to be ashamed of yourself.
was that any model that was standard in Aatu's
sense is isomorphic to a model which is standard in my sense.
Does it or does it not go withOUT saying that ANY
model that is isomorphic TO ANY standard model
is standard BECAUSE of that isomorphism?!?
That depends whether you're using Aatu's definition or mine,
obviously.
And is THAT or is it not THE THEOREM that you had previously
claimed you were not going to state until my attitude improved?
The theorem is that any model that is standard in Aatu's sense is
isomorphic to a model that is standard in my sense.
And if it is so "easy" (as you claimed), then WHY isn't THE REST
of this message A PROOF of it INSTEAD OF an attack
It's pretty easy, yes. Don't you order me around, you obnoxious little
twit. Aatu's already outlined a proof. The question you should be
asking is not, why haven't I proved it, but rather, why should I
devote my valuable time and energy into giving you free tutoring and
presenting a proof that you can understand, when you're behaving in
this way? If you want me to do that, then cut out the attitude and ask
me nicely.
Aatu's remarks are not in tension with this.
Of course not, but THIS is considerably CLEARER than THAT!
I may occasionally make remarks that are a little unclear to some
people the first time around. I am happy to make efforts to clarify
what I am saying if I am asked politely.
And it explains why I feel
justified in saying "the definition is good enough".
AFter the fact, that is easy.
20/20 hindsight is hardly an excuse for waxing abusive.
This post you are replying to was not remotely abusive. I am perfectly
justified in being abusive to you, you are a tiresome obnoxious prat.
It is HARD to see how isomorphism IS EVEN REMOTELY relevant
in ANY case! WTF does Rupert think "models of ZFC" ARE BUILT
out of?? WHERE does he think the DOMAIN of ANY model of ZFC
*comes* from??
A model of ZFC is an ordered pair (M,E), where E is a binary relation
on a set M, satisfying some structural constraints.
The fact that you are ALLEGING THAT M IS A SET implies that
M must be *A*MEMBER*OF*THE*DOMAIN*OF*SOME*MODEL*
*OF*SOME*SET*THEORY*, !@#$%^&.
The universe of sets is the universe of sets. We don't need to step
outside it and have it be a model of ZFC living in a larger universe.
That's irrelevant and unnecessary.
One would EXPECT, if not DEMAND, that THAT theory be ZFC.
MUCH MORE to the point, given that E, being a binary relation from
a model of a set theory, IS ITSELF A SET OF ORDERED PAIRS,
there is NO available justification for M *at*all*: M IS JUST DOM(E),
!@#$%^&.
Sure, since in models of ZFC every set is a member of another set, we
could code for the model with just E. That's a trivial and utterly
uninteresting point, and it's hardly something to start swearing
about.
ZFC IS THE DEFAULT MODEL THEORY FOR FOL *IN* *GENERAL*!!
The MOST usual answer to the question I just asked is
"From a set in a BIGGER model of ZFC."
ZFC is not a model theory.
OK, if you insist, it is a model construction language, in which
the-model-theory-of-FOL is usually conducted.
ZFC *is* a theory. One CAN conduct FOL-model-theory as
a subtheory of ZFC. One often DOES, in fact.
But where are you going with all this? What's your point? What's wrong
with just working in ZFC, without constantly stepping up one level and
saying "Everything here is taking place in a model of ZFC". That's how
you do mathematics. There was nothing wrong with my definition.
There's no need to confuse the issue with all this babble about "inner
models" and "outer models". My definition was perfectly
straightforward, and impeccably stated. After abusing me for lack of
clarity, when I expressed surprise that you found it unclear, you
accused me of being abusive. Where the hell do you think you get off?
Which is why your allegation that I was "babbling"
when I mentioned "the outer model" is
evidence of YOUR attitude problem.
No, it's not.
Yes, it is.
That's not an argument, George. This talk about the "outer model" is
just babble. It's completely irrelevant. A standard model is a model
(M,E) where E is the standard membership relation on M. End of story.
You don't have to think to yourself "Oh, and M lives in a larger model
of ZFC." That's completely irrelevant and unnecessary and just
confuses the issue.
He's trying to help you with your deep-seated confusion.
I am UNconfusing YOU about this RIGHT NOW, !~@#$%^&.
This is a point on which *I* was *LESS* confused than you were,
as was loudly demonstrated by YOUR need to ASK questions.
I'm afraid not, George. There is no point on which you are less
confused than I am. You have nothing to teach me.
You really should try to be more receptive when people are trying to
help you.
You really should just admit that I was right and you were wrong.
Why should I admit that when you're talking palpable nonsense?
You might end up actually learning something, instead of
"putting on a clown shown" as abo so aptly calls it.
I was not the one who NEEDED to learn something here.
You and AK needed to learn that there was an outer model.
There isn't. The universe is just the universe, and there's no need to
mention it every time you state a theorem. This talk about an outer
model is just irrelevant crap.
I DID understand your original statement of your criterion, better
than you did, apparently.
Nope.
What I did not understand was the sense
in which it was or needed to be or could be proved to be equivalent to
the other sense.
Well, I could help you out there, if you were capable of understanding
mathematics. I'm happy to give it a try if your attitude improves.
Given that your version is so much simpler, I also
did not understand how AK failed to get the memo that 'the standard
DEFINITION
of what it means for something to be a standard MODEL" of ZFC had
CHANGED.
You graduated more recently than either DMC or AK and it would stand
to
reason that you would be more aware of a stylistic change like that,
EVEN
if, up to isomorphism, it was NOT a change.
I'm self-taught in mathematical logic and set theory, my university
doesn't offer courses in it. The definition I gave comes from Cohen's
1964 book. It really doesn't matter which one you use.
But THAT, as I said, IS
A RELEVANT THEOREM, and the people to whom it needed to be proved
ARE THE PEOPLE WHO WERE STILL USING THE *OLD* DEFINTION!
The proof is trivial to anyone who knows the subject. If you want to
see the proof, stop all this tiresome shouting and insulting and
politely ask us to help you.
.
- References:
- Re: Countable models of ZFC
- From: george
- Re: Countable models of ZFC
- Prev by Date: Re: Countable models of ZFC
- Next by Date: Re: Countable models of ZFC
- Previous by thread: Re: Countable models of ZFC
- Next by thread: Re: Countable models of ZFC
- Index(es):
Relevant Pages
|
