User blog:Hyp cos/Question about weak compactness

I compared OCFs with my array notation, but stopped at a weakly compact cardinal because I didn't understand how weak compactness works. Could someone help me about these questions: I would understand and remake this after those questions.
 * 1) Weakly compact cardinals have many equivalent definitions, but what's a (set theoretical) definition of "weakly compact property" over a series of ordinals? This may be similar to "weakly inaccessible property" (to be a limit of a series of ordinals) and "weakly Mahlo property" (the set of a series of ordinals in that ordinal is stationary).
 * 2) If weak inaccessibility corresponds with recursive inaccessibility as a "recursive analogue", weak Mahloness corresponds with recursive Mahloness, and \(\Pi_n^1\)-indescribable cardinals correspond with \(\Pi_{n+2}\)-reflecting ordinals, then what does the "weakly compact property" in 1 correspond with?
 * 3) Continue upwards, are there "\(\Pi_n^1\)-indescribable properties" over a series of ordinals (similar to 1)? And what do they correspond with (similar to 2)?