Re: ZFC in 4 Axioms.

zuhair wrote:
I am not understanding this, union and pairing are theorums in this
theory, not axioms.

Perhaps they are and perhaps you proved them earlier in this thread.
But I'm coming in at this point fresh with your revised axioms. If you
like, you may post your proofs of union and pairing from your revised
axioms.

Your P is not followed by (y), why?

Most authors include '(y)' as you have, but it is not strictly
necessary, so I prefer to omit it in order to have a cleaner
formulation. However, we should be very specific as to what YOU mean by
'(y)'. Do you mean that y MUST occur free in the formula P(y)? Usually,
such formulations do not require that y MUST occur free in the formula.
But if do require that y occurs free in the formula, then you must
mention that. Also, are there any restrictions as to the variable x
occurring free in the formula P(y)?

However I discovered the the exclusion by ~y=V is not enough for this
theory.
I need to exlude every set that fulfills its inclusive formula.

i.e X: (A x in X<-> P(x) ) /\ P(X) <-> X is embeded.

and then I will write comprehension as follows:

Ax.3)Comprehension: Ex Ay ( yex<->(P(y) /\ ~ y=x /\ ~(y is embeded) )"

Then please FORMALLY define 'is embedded' or declare it to be
primitive. (Doing neither leaves it primitive by default.)

Why have you still not learned that you have to define EVERY predicate
and/or operation symbol that is not primitive?

MoeBlee

.

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