A How is Inaccessible Cardinal Written?

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Inaccessible cardinals lack a widely accepted notation, though symbols like Theta and phi have been suggested. The discussion references the Absolute Infinite, symbolized by Omega, introduced by Cantor, but notes that it may not align with the concept of inaccessible cardinals. The concept of Absolute Infinity raises philosophical questions about its nature and implications, particularly regarding operations like multiplication. The participants express confusion about the coherence of Absolute Infinity and its inconceivable aspects. Overall, the conversation highlights a gap in formal notation for inaccessible cardinals and the philosophical complexities surrounding infinity.
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I'm writing some notes on set theory, Aleph Null, etc., and was wondering if there's a Notation or Symbol that abbreviates this (inaccessible/strong/uncountable etc. cardinals). I'm not sure if I've seen notation before but it seems like symbols resembling Theta and phi have been used.
 
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I have been to that wiki article and could not find where it labeled itself symbolically.

Did find this: under this other wiki article: https://en.wikipedia.org/wiki/Absolute_Infinite
"The Absolute Infinite (symbol: Ω) is an extension of the idea of infinity proposed by mathematician Georg Cantor.

It can be thought as a number which is bigger than any conceivable or inconceivable quantity, either finite or transfinite.
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However I don't think Cantor or infinite series mathematicians believe the omega from absolute infinite is the same as an uncountable/strong inaccessible cardinal.
Correct me if I am mistaken?
 
I have no expertise in this area. However, the concept of Absolute infinite sounds weird to me. What is Absolute infinity times 2? etc.
 
if it didn't sound weird, how could it possibly be inconceivable? There's a philosophy term for this stuff "Noumenal" stuff we aren't supposed to make sense of.
 
I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...
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