Author: ZaljoharZaljohar
Date: Jan 19, 2008 07:12
Hi all,
Just add the primitive 1-place predicate symbole 'loop' to the list of
primitives of ZF-Regularity.
Now add ( to ZF-Regularity) the axiom
Ax( loop(x) -> (x is singlton & Ey(yex & loop(y))) ).
and add the axiom:
Ex: loop(x).
So informally speaking x would be a set that has one member y that has
one member y' that has one member y'' and so on infinitely, I call
that as x having omega singlton membership chain, so this set clearly
violate regularity.
Now is there a problem with the above axiomatization, I mean doesn't
it violate recursion theory or first order logic?
Second, would x be unique? if so then it is easy to see x is actually
Quines atom Q={Q}.
Can anybody prove that x is unique?
Zuhair
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