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From: Wasell <wasell@example.com>
Newsgroups: sci.logic
Subject: Re: This makes all Analytic(Olcott) truth computable --- ZFC
Date: Thu, 22 Aug 2024 11:55:51 +0200
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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,
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.)