Re: 2nd order replacement and non-standard models of ZF?
- From: Chris Menzel <cmenzel@xxxxxxxxxxxxxxxxxxxx>
- Date: Mon, 2 Mar 2009 17:32:08 +0000 (UTC)
On 02 Mar 2009 17:17:16 +0200, Aatu Koskensilta
<aatu.koskensilta@xxxxxx> said:
Chris Menzel <cmenzel@xxxxxxxxxxxxxxxxxxxx> writes:
The L-S theorem alone entails only that ZFC has a countable model IF
it has a model at all, on which point the theorem is silent. You
need the firepower Aatu notes to prove that ZFC in fact has a model
and to define what it means for such a model to be non-standard.
Why do you think impredicative comprehension is needed to define what
it means for a model of ZFC to be non-standard? (Full impredicative
comprehension is of course an overkill for the existence of a model of
ZFC; Delta-1-1 comprehension will do.)
Ever the stickler, Aatu! I wasn't really thinking precise details here.
The point of my response to George was simply that L-S alone wasn't
sufficient to prove the existence of nonstandard models of ZFC, contrary
to what he had asserted. I suppose "more firepower" rather than "the
firepower Aatu notes" would have been a more appropriate wording.
.
- Follow-Ups:
- Re: 2nd order replacement and non-standard models of ZF?
- From: Aatu Koskensilta
- Re: 2nd order replacement and non-standard models of ZF?
- References:
- Re: 2nd order replacement and non-standard models of ZF?
- From: greeneg
- Re: 2nd order replacement and non-standard models of ZF?
- From: Chris Menzel
- Re: 2nd order replacement and non-standard models of ZF?
- From: Aatu Koskensilta
- Re: 2nd order replacement and non-standard models of ZF?
- Prev by Date: Re: 2nd order replacement and non-standard models of ZF?
- Next by Date: Re: 2nd order replacement and non-standard models of ZF?
- Previous by thread: Re: 2nd order replacement and non-standard models of ZF?
- Next by thread: Re: 2nd order replacement and non-standard models of ZF?
- Index(es):
Relevant Pages
|
