This paper will define a new cardinal called aStationary Cardinal. We will show that every weakly∏11-indescribable cardinal is a stationary cardinal, every stationary cardinal is a greatly Mahlo cardinal and every stationary set of a stationary cardinal reflects. On the other hand, the existence of such a cardinal is independent of that of a∏11-indescribable cardinal and the existence of a cardinal such that every stationary set reflects is also independent of that of a stationary cardinal. As applications, we will show thatV=L implies ◊κ1 holds if κ is∏11-indescribable and so forth.
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