Re: Replacement of Cardinality (ubiquitous ordinals, integer continuum, linear continuum, continuity)

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:

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about ubiquitous ordinals

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What are ubiquitous ordinal?
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Well, you know that ORD, is, the order type of ordinals,
and so it's an ordinal, of all the ordinals.
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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.
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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.
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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.
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So, "ubiquitous ordinals" is exactly what it says.
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