Re: Small Set Theory,Updated.


MoeBlee wrote:
zuhair wrote:
x is a set <-> EP(Ay(yex<->(P[y]&~y=x))).

would that be an incoherent statement?

First, is the expression well formed (or at least a rendering of a well
formed formula)? To answer that question, I would need to know the
formation rules of the language. The expression is not a rendering of a
well formed formula in a first order language. But I do know of
formation rules for a second order language that yield that the
expression is a rendering of a well formed formula. But I don't know
whether you intend for the expression to be in such a second order
language.

MoeBlee

Ok, Moe

let me see this then.

take the following statement:

Ay(yex<->(P[y]&~y=x))

I think this is an expression that is a well formed formula in a first
order language. One look to the axiom of separation in ZFC (which is a
well formed formula in first order language) makes me think that the
formula I've wrote above is a first order language formula.

Instead of writing all of this formula which is a long formula, I made
an equivalent formula to it
to short it. and I call it " x is P_defined". so for example instead of
writing
Ex(Ay(yex<->(P[y]&~y=x))), you can write it as Ex(x is P_defined).
That's all. what is vague about that?

I am sure that Ex(x is P_defined) is a first order language well formed
formula. Why not?
so is most of the complex formulae I wrote in this theory.

Zuhair

.

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