Re: Countable models of ZFC

On Sep 26, 5:35 am, Rupert <rupertmccal...@xxxxxxxxx> wrote:
I'm sorry you had so much trouble understanding it. It seems pretty
straightforward to me. Given a set M,

Well, WHICH are we being given?? A SET?? OR A MODEL??

the standard membership relation
on M is {(x,y):x, y in M and x in y}.

Up to this point, M is a set.

So a model (M,

And THERE is the problem.
Now, SUDDENLY, M is a model INSTEAD OF a set.
Or rather, M is the domain of a model.

If M is both a set AND the domain of a model
then IN ADDITION to the model (M,whatever),
THERE MUST EXIST ALSO
the model OF SOME SET THEORY in which M is a set,
and that model must have a domain of which M is a member.
THAT MODEL ALSO has a membership relation,
and THAT MODEL ALSO might be standard OR NONstandard.
IF THAT model was nonstandard then merely restricting its membership
relation to some submodel IS NOT going to guarantee that that submodel
(in this case, (M,E)) is standard. SOME nonstandard models DO have
nonstandard submodels.

.

Relevant Pages

  • Re: Countable models of ZFC
    ... and THAT MODEL ALSO might be standard OR NONstandard. ... standard. ... You have to be able to make sense of "x is a member of y" all by ... relation to some submodel IS NOT going to guarantee that that submodel ...
    (sci.logic)
  • Re: Formatting a real with an I edit descriptor.
    ... can do this in a standard way with the transferintrinsic. ... equivalence statement. ... (Well I think this is nonstandard. ... The compiler could detect the undefined case as an error and report ...
    (comp.lang.fortran)
  • Re: Fortran
    ... > The F66 standard says something like the value is undefined. ... If something is nonstandard, ... variables is nonstandard and indeed won't compile at all with some ... If something gives a processor-dependent result, ...
    (comp.lang.fortran)
  • Re: Formatting a real with an I edit descriptor.
    ... Others have commented about what "correct" might mean with a nonstandard ... and modintrinsics, they all do similar but different things. ... can do this in a standard way with the transferintrinsic. ... equivalence statement. ...
    (comp.lang.fortran)
  • Re: Non-standard arithmetic
    ... is that the usual rules of arithmetic apply to the nonstandard ... the standard elements and nonstandard (infinite) elements. ... The intended interpretation of the Peano Axioms is that the variables ...
    (sci.logic)