Having κ many inaccessibles below κ places κ far beyond any finitely indexed position in the inaccessible hierarchy

(3.3) Suppose κ is inaccessible. Then κ is weakly compact  ⇔  L(κ,ω) is weakly κ-compact. Also, Also κ is weakly compact ⇒ there is a set of κ inaccessibles before κ. Thus a weakly compact inaccessible cardinal is exceedingly large; in particular it cannot be the first, second, …, nth, … inaccessible.