Re: This makes all Analytic(Olcott) truth computable --- ZFC

On 2024-08-22 09:55:51 +0000, Wasell said:

On Wed, 21 Aug 2024 07:37:50 -0500, in article <va4n2u$3s0hu$3@dont-email.me>,
olcott wrote:

On 8/21/2024 3:54 AM, Mikko wrote:

On 2024-08-20 13:59:42 +0000, olcott said:
 

On 8/20/2024 5:21 AM, Mikko wrote:

 [...]
 

Set theories with an unversal set need to restrict
the construction operations more than what is usually considered
reasonable.

 I don't see how. The set of all sets that do not contain
themselves simply becomes the set of all sets.

 The set of all sets that do not contain themselves is the Russell set
that revealied the inconsistency of the naive set theory. The main
improvment in ZF was the non-existence of this set.

 So basically you agreed with me on everything.

 Oh, you blithering imbecile! The universal set V is, by definition,

Often U is used instead of V for the universal set. V is often the
smallest set that conains the empty set and every set that can be
constructed from other members of V.

an element of itself. It is a set, and therefore an element of the
set of all sets.
 By Specification, we can split V into the set of all sets that have
themselves as an element, and its complement, the set of all sets
that are not elements of themselves. Neither of these two sets are
empty.
 Do you see where this is going? Or do you need more hand holding?
 There are set theories with a universal set, but they also
have restricted Specification. (Or, more commonly, no Axiom of
Specification, but a restricted Comprehension instead.)

If every set has a power set then the univesal has a power set, too,
and the power set of the universal set is a member of the univerasl set.
One must be careful with axioms or one can prove someting false from
the exstence of a set that has its poverset (and the power set of its
powerset) as a member.
--
Mikko