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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: Wed, 1 Jan 2025 10:10:05 -0800
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On 07/29/2024 12:46 PM, Ross Finlayson wrote:
> 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".
>