Re: ZFC in another shape.

On Feb 5, 3:00 pm, "zuhair" <zaljo...@xxxxxxxxx> wrote:
On Feb 4, 10:41 pm, "Rupert" <rupertmccal...@xxxxxxxxx> wrote:





On Feb 5, 1:02 pm, "Jesse F. Hughes" <j...@xxxxxxxxxxxxx> wrote:

"Jesse F. Hughes" <j...@xxxxxxxxxxxxx> writes:

"zuhair" <zaljo...@xxxxxxxxx> writes:

Hi All,

Is the following theory equivalent to ZFC?

Theory X.

Primitives: e,=

Definition Schema:

x is an ordinal <-> AmAn(((mex&nem)->nex)&Az(zen->zem)).

You sure that's the right definition? As consequence of this
definition, you get:

x is an ordinal -> AmAnAz(z e n -> z e m)

How is that? I think you are mistaken. See my answer to your previous
post.


No, he's correct. This is because from

P<->AmAn(Q&R)

you can infer

P->AmAnR

You really need a lot of practice in logic. For now it would probably
be best to accept that when more experienced people claim mistakes in
what you've done it's very unlikely that they're wrong. Just put your
mind to trying to understand what they're saying.

I only wanted to say that x is an ordinal iff
x is transitive and every member in x is transtive.


Okay, fine. Well, you didn't write it up correctly. That should be

x is an ordinal <-> AyAz((y e x & z e y) -> z e x) & Ay(y e x ->
AzAw((z e y & w e z) -> w e y))

which is a very well known definition of ordinals.


It's not obvious to me that this is equivalent to the usual
definition. The usual definition is that an ordinal is transitive and
connected, i.e. for all x and y in the ordinal we have either x e y or
x = y or y e x.

Anyhow perhaps I wrote it in a mistaken way.


Yes, you did.

.

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