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NNTP-Posting-Date: Mon, 29 Jul 2024 19:46:05 +0000
Subject: Re: Replacement of Cardinality (ubiquitous ordinals, integer
 continuum, linear continuum, continuity)
Newsgroups: sci.logic,sci.math
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Mon, 29 Jul 2024 12:46:23 -0700
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On 07/29/2024 12:44 PM, Ross Finlayson wrote:
> On 07/29/2024 05:32 AM, Jim Burns wrote:
>> On 7/28/2024 7:42 PM, Ross Finlayson wrote:
>>> On 07/28/2024 04:32 PM, Ross Finlayson wrote:
>>>> On 07/28/2024 04:25 PM, Ross Finlayson wrote:
>>>>> On 07/28/2024 11:17 AM, Jim Burns wrote:
>>
>>>>>> [...]
>>>>> [...]
>>>> [...]
>>>
>>> about ubiquitous ordinals
>>
>> What are ubiquitous ordinal?
>>
>>
>
> Well, you know that ORD, is, the order type of ordinals,
> and so it's an ordinal, of all the ordinals.
>
> The "ubiquitous ordinals", sort of recalls Kronecker's
> "G-d made the integers, the rest is the work of Man",
> that the Integer Continuum, is the model and ground
> model, of any sort of language of finite words,
> like set theory.
>
> It's like the universe of set theory, then as that
> there's _always_ an arithmetization, or as with regards
> to ordering and numbering as a bit weaker property than
> collecting and counting, so that "ubiquitous ordinals"
> is what you get from a discrete world.
>
> Then there's that according to the set-theoretic Powerset
> theorem of Cantor, that when the putative function is
> successor, in ubiquitous ordinals where order type is
> powerset is successor, then there's no missing element.
>
> So, "ubiquitous ordinals" is exactly what it says.
>
>

Or, you know, "infinity plus one".