Axiom schema of Hyperfinity

Hi all,

Define: Tc(x)= U{x,Ux,UUx,UUUx,........}

Define: x is finite <-> EREconvR( R is well ordering on x &
convR is well ordering on x ).

Define: x is hyperfinite<->(x is finite & Ay( yeTc(x) -> y is
finite)).

I suggest adding the following axiom schema to the axioms of
ZF:


Axiom schema of Hyperfinity:If F is a formula in which x is not free,
then all closures of


ExAy(yex<->( y is hyperfinite & F(y) ) )


is an axiom.


Is there anybody who think that this schema is inconsistent with
ZF? or is the above schema a theorem schema of ZF?

Any help regarding that?


Zuhair

.

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