Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Topic: ZFC is shown to be inconsistent
Replies: 6   Last Post: Jun 6, 2014 1:00 PM

 Messages: [ Previous | Next ]
 byron Posts: 891 Registered: 3/3/09
ZFC is shown to be inconsistent
Posted: Jun 5, 2014 8:09 AM

australias leading erotic poet colin leslie dean has shown ZFC to be
inconsistent

an axiom of ZFC ie axiom of separation outlaws itself thus making ZFC
inconsistent

proof
http://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory

3. Axiom schema of specification (also called the axiom schema of
separation or of restricted comprehension): If z is a set, and \phi\!
is any property which may characterize the elements x of z, then there
is a
subset y of z containing those x in z which satisfy the property. The
"restriction" to z is necessary to avoid Russell's paradox and its
variant

now Russell's paradox is a famous example of an impredicative
construction, namely the set of all sets which do not contain
themselves

the axiom of separation is used to outlaw impredicative statements

but this axiom of separation is itself impredicative
http://math.stanford.edu/~feferman/papers/predicativity.pdf

"in ZF the fundamental source of impredicativity is the seperation
axiom which asserts that for each well formed function p(x)of the
language ZF the existence of the set x : x } a ^ p(x) for any set a
Since the formular
p may contain quantifiers ranging over the supposed "totality" of all
the sets this is impredicativity according to the VCP this
impredicativity is given teeth by the axiom of infinity "

thus it outlaws itself