Re: ZFC in 4 Axioms.


MoeBlee wrote:
zuhair wrote:
ExAy yex<->P(y). is y here free or bounded?

Which 'y'? There are two of them, plus any finite number of them in
P(y).

And do you mean:

ExAy yex<->P(y)

or do you mean:

ExAy(yex <-> P(y)).

Then figure out for yourself what is free and bound.

MoeBlee

The only objection I Have to this is that I saw many in this forum
write both of these to mean the same thing. Perhaps I got it wrong.

Anyhow I am developing a new line of thinking about my small set
theory.

here is a trial.

-Small Set Theory-

Primitive e

Definition:

Ax(x is P_embeded <-> (Ay: y e x <-> P(y)) /\ P(x))

1)Extensionality: As in ZFC
2)Comprehesnion: ExAy ( yex <-> (P(y) /\ ~( x is P_embeded)) )
3)Infinity: As in ZFC.

Of course all theorums that I have wrote before should be corrected
after the correction of 2).

This theory has a universe, all its sets are well founded and the set
of all ordinals is a set
In other manner it escapes all known paradoxes.

Smiles

Zuhair

.

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