Berkeley Cardinals

[Another_Council]

Simply put, how do Berkeley Cardinals even work?

 

[Timeless]

no ******* clue. All I know is that they are on some beyond transcendent of ultra manifold level

 

[Guardian_Doge]

Simply put, how do Berkeley Cardinals even work?

I am unaware of the specifics especially because I don't have years of knowledge on set theory, but they're just the biggest kind of large cardinal, to the point where 0 = 1 axiom begins to fail. So yeah timeless is pretty much right, they're incredibly so much higher than Woodin Cardinals.

 

[Another_Council]

Jesus

 

[Greatsage13th]

Anything higher than Berkeley's cardinal?

 

[Lilixa]

Anything higher than Berkeley's cardinal?

i think this https://en.wikipedia.org/wiki/Absolute_Infinite

 

[Lilixa]

probably higher than absolute infinite ? https://en.wikipedia.org/wiki/Extended_modal_realism

 

[Greatsage13th]

i think this https://en.wikipedia.org/wiki/Absolute_Infinite

I remember at one point, this was what tier 0 is labelled as.

probably higher than absolute infinite ? https://en.wikipedia.org/wiki/Extended_modal_realism

Definitely

 

[Timeless]

Absolute Infinity can't really be applied to a tier due to it being bigger than any number or anything that can be conceptualized using mathematics. So it would be on the level of the Mathiverse, which itself can't be applied to a tier (the tier 0 rating is a server understatement). Extended modal realism is... weird

 

[Guardian_Doge]

there's different axioms for absolute infinity, ZFC has one, NBG set theory as well, Von neumann universe of sets as well, 0=1 axiom ETC
But that's for another day.

Also yeah I guess extended modal realism is > it, assuming that it's > type 4 multiverse which is likely equal to Ultimate V=L Conjecture, which states no infinity can reach it.

 

[Timeless]

what exactly is the icarus set btw?

 

[SheevShezarrine]

Honestly I thought this thread was about a sports team for a sec

 

[Guardian_Doge]

what exactly is the icarus set btw?

Vλ+2 − L(Vλ+1), it's called the suicide cardinal, I have some relevant links I can dm you, if you'd like.

 

[Greatsage13th]

Vλ+2 − L(Vλ+1), it's called the suicide cardinal, I have some relevant links I can dm you, if you'd like.

why is it called suicide cardinal?

 

[Guardian_Doge]

why is it called suicide cardinal?

Mainly a reference to the legend of Icarus where he flew so close to the sun, it essentially was an act of suicide. (In math terms, its equivalent is transcending so many degrees of infinity to such an absurd degree enters such a paradoxical environment it breaks anything down. Which is important because of cataphysics being the defiance of nature.)

 

[Greatsage13th]

Mainly a reference to the legend of Icarus where he flew so close to the sun, it essentially was an act of suicide. (In math terms, its equivalent is transcending so many degrees of infinity to such an absurd degree enters such a paradoxical environment it breaks anything down. Which is important because of cataphysics being the defiance of nature.)

I see

 

[ImNot4nUser]

I find funny how your average battleboarder discovers that math is more OP than any meta-fictional verse

 

[Timeless]

how does the icarus set compare to thinks like rank-into-rank cardinals and Berkeley cardinals

 

[Guardian_Doge]

how does the icarus set compare to thinks like rank-into-rank cardinals and Berkeley cardinals

Well it is purely defined as anything beyond Rank-Into-Rank (I0-I3) since it already breaks down 0=1 theorem which is > the former.
But yeah like i said, an icarus sets purpose to be as high as something can get in set theory. Though it'd be much easier to dm the explanations.