Inaccessible Cardinal vs Mahlo Cardinal

[MightyFrogBeyond]

Context: I’m familiar with the Inaccessible Cardinal thanks to Vsauce’s brief coverage of the concept. For my personal cosmology, I’m going to use the hierarchy between the Inaccessible Cardinal and the Mahlo Cardinal as a power system for my characters to escalate in power from.

Question 1: Is there a difference between a Mahlo cardinal and a “weak” Mahlo Cardinal? Are there other versions of Mahlo Cardinals?

Question 2: What comes “after” the Inaccessible Cardinal? Is it 2^Inaccessible Cardinal? Much like Aleph 2 is compared to Aleph 1.

If you have any information, please post below. Thank you.

 

[Vietthai96]

List of large cardinal properties - Wikipedia

en.m.wikipedia.org

 

[MightyFrogBeyond]

List of large cardinal properties - Wikipedia

en.m.wikipedia.org

I’ve read the Mahlo Cardinal section. It seems what I’m looking for is strongly Mahlo Cardinal.

Now, how can I create a power system between Inaccesible Cardinal and Strongly Mahlo?
I’ve read the section but I either don’t comprehend the terminologies+symbols and text or,
the difference between the two isn’t mentioned.
Do you know what I could do?
My idea of a power system between the two would be like the alephs and the Inaccesible Cardinal.
So, Inaccessible Cardinal-1, 2, 3, 4 etc.

 

[MightyFrogBeyond]

Bump