User blog comment:Hyp cos/Question about weak compactness/@comment-35470197-20180911215601/@comment-11227630-20180913050650

> Then the "2-weak compactness" is equivalent to the property that it is a weakly compact cardinal which is a limit of weakly compact cardinals.

That's quite weak. For the use of OCF, one may need such property that Are there any other definition of "weakly compact property" suit this?
 * A 2-weakly compact cardinal has the "weakly compact property" over weakly compact cardinals.
 * The least 2-weakly compact cardinal would be "Mahlo over weakly compact cardinals" (i.e. the set of weakly compact cardinals below it are stationary), Mahlo over these kind of ordinals (i.e. the set of weakly compact cardinals that are "Mahlo over weakly compact cardinals" below it are stationary), and so on; and it's large enough for collapsing over those Mahloness over weakly compact cardinals.

> Are you the author of the document you linked?

Certainly no. I do not understand it, especially the parts except the OCF.