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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 like Russells paradox
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 thus ZFC contradicts itself



