Re: ZFC in 4 Axioms.


zuhair wrote:
Primitive e
Ax.1) Extensionality: As in ZFC
Ax.2) Universe: E!V Ay yeV
Ax.3) Comprehesnion: Ex Ay ( yex<->P(y) /\ y!=x /\ y!=V )
Ax.4) Infinity: As in ZFC
Ax.5) Choice: As in ZFC.

Are we starting all over again? If so, then, since you don't have union
and pairing axioms, your axioms of infinity and choice will have to be
in primitive notation, or you'll have to show how to defined '0',
singleton, binary union, 'is a function' and functional notation from
your axioms 1-2.

"Comprehesnion: Ex Ay ( yex<->P(y) /\ y!=x /\ y!=V )"

You're lacking a needed pair of parentheses.

Do you mean:

ExAy(yex <-> (P & ~y=x & ~y=V)).

Also change 2 to this:

E!vAy yev.

Then define:

V = the unique v such that Ay yev.

MoeBlee

.

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