Re: A question about ackermann's set theory.

On Oct 30, 3:47 pm, Rupert <rupertmccal...@xxxxxxxxx> wrote:
On Oct 31, 5:43 am, Zaljo...@xxxxxxxxx wrote:





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!

Is it? I don't know, I don't know Ackermann set theory very well. Can
you elaborate on exactly where the inconsistency comes in?

Yes, this is clear! the set of all ordinals in V cannot be in V, since
if then
it would be an ordinal in V, and thus in itself, contradicting
Regularity for sets.

Zuhair



but I must be wrong.

So were is my error?

Zuhair- Hide quoted text -

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