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Re: IMPROVED AXIOM OF REGULARITY... <X1 e X2 e X3 .. e Xn e X1>
Posted:
May 8, 2012 11:11 PM
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> -------AXIOM OF REGULARITY II------
>
> AXIOM OF TRANSITIVITY
> A(X) A(Z) X t Z <-> (X e Z) v E(Y) (X e Y) ^ (Y t Z)
>
> AXIOM OF REGULARITY
> A(X) A(Z) (X t Z) -> ~(X e Z)
>
> -----------------------------------
This suggests an:
AXIOM OF WEAK REGULARITY
A(X) A(Z) (X t Z) -> ~(Z e X)
which will allow a directed acyclic graph of set membership
this is a more general network than a hierachy of set ranks.
e.g.
1 e SINGLETONS
SINGLETONS e MATHS_TERMS
1 e MATHS_TERMS
A relative rank and order is apparent, without cycles,
though an absolute rank is lost since SINGLETONS is mid-way
between MATHS_TERMS and 1, hence if 1 e MATHS_TERMS was
defined 1st a difference in set rank of 1 would have to be
split to accommodate the set SINGLETONS.
Graham Cooper (BInfTech)
KINGS BEACH QUEENSLAND
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