Re: Countable models of ZFC
- From: Rupert <rupertmccallum@xxxxxxxxx>
- Date: Fri, 05 Oct 2007 23:18:31 -0700
On Oct 4, 8:54 pm, george <gree...@xxxxxxxxxx> wrote:
On Oct 3, 8:35 pm, Rupert <rupertmccal...@xxxxxxxxx> wrote:
For me, models are sets. I don't like talking about proper classes.
Well, tough; you're in sci.logic and we DO class theories here.
I am perfectly entitled to work in ZFC, in which there are only sets,
if I want to. And you are perfectly entitled to say "Excuse me, but I
would like to look at what you are doing from the point of view of a
different theory in which proper classes are allowed" and then specify
what theory you want to work in. You are not entitled to shout and
insult people when it is you who are engaged in semi-coherent ranting.
More to the point, it is utter idiocy for ANYbody who is talking
about models of ZFC to claim he doesn't like proper classes,
because the universe/domain of EVERY model of ZFC *is* a
proper class in the opinion OF THAT MODEL ITSELF!
Rubbish. The language of ZFC doesn't even have quantifiers which range
over proper classes, and the model is not an element of itself, so it
cannot "have an opinion" about itself. It is perfectly reasonable for
someone to talk about models of ZFC and to say they don't like working
with proper classes, and no sensible person would maintain otherwise.
When I say "M is a set", I don't mean it's a set living in some model,
I just mean it's a set, period.
BY DEFINITION, EVERY set MUST be in some larger set, IN
ORDER TO BE a set! IF IT'S NOT in some larger set THEN
IT'S A PROPER CLASS AND NOT a set!
Big... deal. You really like shouting while making utterly trivial and
irrelevant points, don't you?
Yes, there do exist lots of other models which are sets in which M
lives, but there was no particular call to mention any of them, they
are beside the point.
.
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- Re: Countable models of ZFC
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- Re: Countable models of ZFC
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- Re: Countable models of ZFC
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