A very simple upgrade for mahlo cardinals.

[DontTalkDT]

May I ask what you'd use to quantify High 1-A and 0, then, if not large cardinals?

Edit: I'll sent you a DM now that I think about it.

 

[Cat275]

You should read

That did not prove anything nor does it refute my statements you didn't even explain why that's the case, Though I guess I'll leave this matter to the staffs for the time being.

This thread can be closed or stay open if needed.

 

[Qawsedf234]

@Qawsedf234 might also be able to help.

I can help determine usability but if you need me to help determine a mathematical basis I'm not familiar with all the high concept numbers/terms.

 

[Agnaa]

@DontTalkDT @KingPin0422

I am obviously very open to if the two of you can come up with a more specific and rational mathematical definition of Tier 0 via a private discussion thread, preferably while asking @Ultima_Reality and @Agnaa for input.

I would prefer if I am kept informed about your progress though.

I'll copy what I said on my message wall here. From a skim I think I agree with DT, in that I'm neutral.

I didn't deeply read your post since it seems to go heavily into the mathematics in a way that I cannot understand. I only understand the basics of cardinals. But I do still have a response, but since I haven't properly read your thread, I'd only feel comfortable posting it here.

Philosophically, there's many places we could place the borders for High 1-A and 0. And really, wherever we place them, that decision seems pretty arbitrary. There's a certain function we want the tiers 1-A, High 1-A, and 0 to have in how they operate; but the exact mathematical constructs they end up corresponding to depends on what we equalise layers of transcendence within them to, which seems wholly arbitrary. The only verses for which these arbitrary distinctions make a difference are verses which explicitly invoke cardinals in their cosmology. We could have 1-A+ start at R^R^R^omega instead of an omega-length chain of R^R^R...^R. And we could have High 1-A start at R^R^R^R, and 0 start at R^R^R^R^R, and the only verses that would be changed by our choice are these mathematically-invoking verses.

Since it barely matters, and I can't understand it, I don't care what happens. Some people have suggested tier 0 being above ZFC, or having High 1-A involve adding new axioms, with 0 involving entirely new logical systems. I really don't care which suggestion ends up going through.

 

[Antvasima]

I'm very neutral regarding the situation for the time being.

In my eyes, large cardinals being used for High 1-A is already a bad choice, so stacking on top of that with an even higher cardinal (or whatever else) for Tier 0 will also always be a bad choice.
So for the time being (i.e. until I, if ever, talk about our High 1-A choice) I'm neutral regarding all choices for Tier 0, as they don't affect what we equalize to them anyway.

May I ask what you'd use to quantify High 1-A and 0, then, if not large cardinals?

Edit: I'll sent you a DM now that I think about it.

Thank you both for helping out. I would appreciate if you keep me updated in private regarding your progress regarding how to define tier High 1-A and 0.

 

[Antvasima]

I can help determine usability but if you need me to help determine a mathematical basis I'm not familiar with all the high concept numbers/terms.

I'll copy what I said on my message wall here. From a skim I think I agree with DT, in that I'm neutral.

I didn't deeply read your post since it seems to go heavily into the mathematics in a way that I cannot understand. I only understand the basics of cardinals. But I do still have a response, but since I haven't properly read your thread, I'd only feel comfortable posting it here.

Philosophically, there's many places we could place the borders for High 1-A and 0. And really, wherever we place them, that decision seems pretty arbitrary. There's a certain function we want the tiers 1-A, High 1-A, and 0 to have in how they operate; but the exact mathematical constructs they end up corresponding to depends on what we equalise layers of transcendence within them to, which seems wholly arbitrary. The only verses for which these arbitrary distinctions make a difference are verses which explicitly invoke cardinals in their cosmology. We could have 1-A+ start at R^R^R^omega instead of an omega-length chain of R^R^R...^R. And we could have High 1-A start at R^R^R^R, and 0 start at R^R^R^R^R, and the only verses that would be changed by our choice are these mathematically-invoking verses.

Since it barely matters, and I can't understand it, I don't care what happens. Some people have suggested tier 0 being above ZFC, or having High 1-A involve adding new axioms, with 0 involving entirely new logical systems. I really don't care which suggestion ends up going through.

Okay. No problem.

Is there anything left to do here, or should we close this thread then?

 

[Cat275]

It can be closed now I believe.

 

[Antvasima]

I have done so. Thank you to everybody who helped out here.