User blog comment:PsiCubed2/How to make Deedlit's Mahlo-level notation more intuitive/@comment-35470197-20180807000338/@comment-35470197-20180808110307

> No, what I'm saying is deeper than that.

I see. What I should do first is to ask you what the ground (assumed) knowledge is.

> But what "argument" did your linked proofs resolve? You just gave proof to something we already knew. There was never any disagreement about the fact that M>I(1,0,0).

Haha, exactly. Please forget my poor "argument".

> That's all it is. Nothing mysterious or difficult. And certainly nothing to be afraid of.

I agree. Therefore I wrote a natural step-by-step sufficient natural-language-based proof without fancy or mysterious notions. (You may think that I should not have used CH just in order to simplify the argument with reflection, though.)

> I think that exercising our logical ability to prove our own personal claims is far more useful then retreading complicated proofs of basic things we already know.

Ok. I will do so. Thank you for the advice.

> You're apparently better in set theory than me, because I haven't understood what you just said.

Not exactly. I know few about Mahlo. It is absolutely difficult. To be more precise, I know few about Deedlit's OCF. I could not imagine why it goes beyond so far without using the strategies in Rathjen's paper, which looks very important for its strength. Isn't it surprising that he extended such a Mahlo-level OCF to ordinals greater than M^\Gamma? The restriction of Rathjen's OCF to M^Gamma is essential, because he strictly use the map kappa -> kappa^- in order to ensure the strength of psi_{chi_a(0)}. (At last, I asked to him, because it is his theorem.)

> The good news is that the precise properties of Mahlos don't really matter for understanding their use in collapsing fuctions (they are necessary to justify what people like Rathjen and Deedlit are doing, but not to understanding how these systems work).

Ok. It is actually a good news if it is correct.