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Topic: IMPROVED AXIOM OF REGULARITY... <X1 e X2 e X3 .. e Xn e X1>
Replies: 26   Last Post: May 12, 2012 5:13 PM

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 Graham Cooper Posts: 4,039 Registered: 5/20/10
Re: IMPROVED AXIOM OF REGULARITY... <X1 e X2 e X3 .. e Xn e X1>
Posted: May 8, 2012 11:11 PM

> -------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

Date Subject Author
5/8/12 Graham Cooper
5/8/12 Graham Cooper
5/9/12 MoeBlee
5/9/12 Graham Cooper
5/9/12 MoeBlee
5/9/12 Graham Cooper
5/10/12 MoeBlee
5/10/12 Graham Cooper
5/10/12 MoeBlee
5/10/12 Graham Cooper
5/11/12 MoeBlee
5/11/12 MoeBlee
5/11/12 Graham Cooper
5/11/12 MoeBlee
5/11/12 Graham Cooper
5/11/12 MoeBlee
5/11/12 Graham Cooper
5/11/12 Graham Cooper
5/11/12 MoeBlee
5/11/12 Graham Cooper
5/11/12 MoeBlee
5/11/12 Graham Cooper
5/11/12 MoeBlee
5/11/12 Graham Cooper
5/12/12 hagman
5/12/12 Graham Cooper
5/12/12 Graham Cooper