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Self-reference ENGINE discussion thread

Berkeley and Reinhardt are above all other large cardinals in Consistency Strength, not sheer size (they might as well be incomparable to the others since they lack axiom of choice so it would be inherently wrong in saying they are bigger than all other cardinals).

Size-wise, the biggest are probably Extendible Cardinals or Ultra-Huge Cardinals.
 
Berkeley and Reinhardt are above all other large cardinals in Consistency Strength, not sheer size (they might as well be incomparable to the others since they lack axiom of choice so it would be inherently wrong in saying they are bigger than all other cardinals).

Size-wise, the biggest are probably Extendible Cardinals or Ultra-Huge Cardinals.
Has sre surpassed all cardinals now?
 
The first hierarchy already reaches the "top" of the large cardinal hierarchy and breached into inconsistency, and considering how we currently equate that to 0=1, then yes it seems to have.
 
Yes. It can't even reach the first hierarchy. The first out of 0=1 among of hierarchies.
So your telling me this verse at the weakest surpasses all of our known cardinals

and then it basically creates new stuff that we haven’t even made yet (aka higher than 0=1, which mathematicians haven’t invented yet)
 
But there are an infinite amount of hierarchies beyond it as well?
Yes, the hierarchy of logic itself is nothing more than a rung within a higher-level hierarchy. And this hierarchy is also a step within another hierarchy, etc and etc.
 
So your telling me this verse at the weakest surpasses all of our known cardinals

and then it basically creates new stuff that we haven’t even made yet (aka higher than 0=1, which mathematicians haven’t invented yet)
Yes

The first hierarchy scales to 0=1, and then there are 0=1 amount of hierarchies above that. And then laplace demon sees all of that as a dream, beyond that is infinite hierarchies of laplace demons. And all of that is just part of one single story. One out of infinite amount. It's even stated there exists infinite possibilities and impossibilities*possibilities and impossibilities ad infinitum.
 
Yes

The first hierarchy scales to 0=1, and then there are 0=1 amount of hierarchies above that. And then laplace demon sees all of that as a dream, beyond that is infinite hierarchies of laplace demons. And all of that is just part of one single story. One out of infinite amount. It's even stated there exists infinite possibilities and impossibilities*possibilities and impossibilities ad infinitum.
Is there a way to surpass this?

And where does blue and white on the cardinal area?
 
Can i ask you something?

Would Von Neumann Ordinals scale to high hyperversal?
With axiom of infinity? That's like 1-A+ (with this amount of dimension) in standard set theory if there as many amount as all the stages.
 
Where do stuff like ω scale? ω+1 etc, ωω and 2ω?
If you mean V(omega) it's just omega in cardinality, V(omega + 1) is just aleph one and things like V(omega omega) is aleph-omega omega.
 
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If you mean V(omega) it's just omega in cardinality, V(omega + 1) is just aleph one and things like V(omega omega) is just aleph-omega.
I am asking this because SRE mentions this stuff and i'm just wondering if Ordinals can be tiered.
 
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