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From: David Chmelik <dchmelik@gmail.com>
Newsgroups: sci.math
Subject: Re: universe set?
Date: Wed, 19 Jun 2024 09:12:41 -0000 (UTC)
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On Tue, 18 Jun 2024 14:33:40 -0700, Ross Finlayson wrote:
> On 06/18/2024 02:29 PM, Ross Finlayson wrote:
>> On 06/18/2024 06:18 AM, FromTheRafters wrote:
>>> David Chmelik has brought this to us :
>>>> On Tue, 18 Jun 2024 12:05:45 -0000 (UTC), David Chmelik wrote:
>>>> Is the universe set called universet?
>>>
>>> Domain of Discourse. Usually a blackboard bold (or doublestruck) D is
>>> the symbol.

I remember that, or 'universe of discourse' but my professors usually just 
wrote the specific set such as N, Z, Q, R, C (in blackboard bold).

>> See for exampler Forster's "Set Theory with a Universal Set".
>>
>> The idea that a universal set exists is called "Domain Principle"
>> or "Domainprinzip".

I see.  I'm not convinced sets exist, or maybe/likely they do, but not 
that set theory rather than number theory should be foundation, such as 
explained by mathematical philosopher Mike Hockney.  Nevertheless, I 
always liked the idea of 'universe set', like the greatest infinity (other 
than the universe set's power set, haha).

>> The domain of discourse is a usual term.
>>
>> See for example Finsler and Boffa, Kunen inconsistency,
>> set of all sets, order type of ordinals, group of all groups,
>> infinite-dimensional space, "Continuum", sometimes just "the world".

Do those authors also call it infinite-dimensional space, or is that your 
elaboration?  Of course, that exists, but I don't know I'd call that a 
set, despite contains everything that exists ideally/mentally/spiritually 
(which contains all 'atoms'/'matter'/'physis' as illusion within).

> https://www.youtube.com/watch?v=aHS0VKOM09U
> 
> "Thomas Forster - Recent developments in Set Theory with a Universal
> Set"
> 
> I don't vouch for this yet it's part of the study, about things like
> "New Foundations with Ur-Elements" or "New Foundations with Universes"
> and so on.

There should be new foundations with numbers, whether considered points/
monads or line segments on the number line, or waves.

> Here's it's "Null Axiom Theory" or "Universal Axiom Theory",
> for example.

Axioms are important, but I noticed for some, if it's unclear what they 
mean, and they're not geometrically demonstrated (like most/all Euclid's, 
and ones from Pythagorean Theorem to Euler's Formula, etc.) then we might 
not know if they ever apply to reality, like I don't 100% know what 
'infinite containers' or 'games' mean in relation to reality.  Those may 
be fun but I prefer ones that describe reality.