[FOM] Generalization Axiom Scheme

Zuhair Abdul Ghafoor Al-Johar zaljohar at yahoo.com
Sat Nov 12 02:00:35 EST 2011

Dear Sirs.

This theory of mine is inconsistent.

Let phi(x) be

(for all y. (y is finite and y supernumerous to z1) -> x hereditarily subnumerous to y)

Let z1 be some infinite set, and we get the set of all sets and thus
reproducing Russell's paradox.

Best regards


On Thu, 3 Nov 2011 10:08:09 -0700 (PDT) I wrote:
> Dear FoMers
> Generalization scheme is an FOL axiom scheme that I coined
> lately, when added to Extensionality, Impredicative
> class comprehension and Pairing it can interpret
> set union, power, separation, replacement and
> Infinity. 
> Of course sets are defined as elements of classes.
> Generalization scheme: for n=0,1,2,3,....; if phi(x) is
>     a formula in which z1...zn are the only
> parameters
>     in it, then:
> [for every z1 is HF ... zn is HF.
> (Exist x. x is a class of HF sets and phi(x)) and
> for every set x of HF sets. (phi(x) -> x is HF)]
> ->
> [for every set z1...zn. for all x. phi(x) -> x is a
> set]
> is an axiom.
> HF stands for the predicate "hereditarily finite".

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