A question about ackermann's set theory.

Hi all,

Ackermann's set theory is present at

http://en.wikipedia.org/wiki/Ackermann_set_theory

One thing I don't understand is the reflection axiom schema

My objection is the following:

Let F(y)<->( yeV & y is ordinal)

Now we have Ay ( (yeV & y is ordinal) -> yeV )

So according the reflection axiom schema we will have

Ex( xeV & Ay( yex <->( yeV & y is ordinal ) )

Which is clearly contradictive!

but I must be wrong.

So were is my error?

Zuhair

.