User blog comment:Hyp cos/Question about weak compactness/@comment-35470197-20180911215601/@comment-11227630-20180912105940

How large is the least "2-weakly compact cardinal" (i.e. the ordinal has the "weakly compact property" over weakly compact cardinals less than it) in the scale of indescribability?

And define: \(\pi\) is \((\alpha_1,\cdots,\alpha_n)\)-weakly compact if it's \((\alpha_1,\cdots,\alpha_i,\beta,\pi,\underbrace{0,\cdots,0}_{n-i-2})\)-weakly compact for all \(\beta<\alpha_{i+1}\) and \(0\le i\le n-2\), and it has "weakly compact property" over the set of \((\alpha_1,\cdots,\alpha_{n-1},\beta)\)-weakly compact cardinals \(<\pi\) for all \(\beta<\alpha_n\). Does the least \(\Pi_2^1\)-indescribable cardinal have all these weak compactness and large enough for collapsing over the weak compactness?