[OleBerg]

Prefixed disclaimer: The logic of the treatment is a little unusual, as the meaning of the third step varies, according to whether the first two steps was used. And to make it even more complicated, both step 1) and 3) may vary, if the bidding had started another way. For instance, here itr is assumed that the 4♠ bidder holds at least one ace, so that if opener has three, enough aces are present.

Anyway I will describe all eight possible sequences, and their meaning. The bidding has started:

1♥ - (3♠) - 4♠

and we assume the opponents pass.

The meaning of openers first bid (after 4♠)

4nt: Three aces. (With or without a spade stopper.)
5♣: Only two aces, and a spade stopper.
5♦: Only two aces, and no spade stopper.
5♥: At most one ace.

Responders first bid after 4nt:

5♣: Spade stopper.
5♦: No spade stopper, but still interested in slam.
5♥. No spade stopper, I have shown my hand fully.

Responders first bid after 5♣:

5♦: I have two aces too, but am not willing to bid slam myself.
5♥: I have only one ace.

Responders first bid after 5♦:

5♥: We are missing somthing crucial, either two aces or a spade stopper.

Openers rebid after 4nt-5♣:

5♦: Still interested in slam.
5♥: Nothing further to add.

Openers rebid after 4nt-5♦:

5♥: We do not have a spade stopper.

You are always allowed to go past 5♥, once you have gathered information that slam is worthwhile.

Suffixed disclaimer: This is difficult stuff, and it would be even more difficult if our suit had been diamonds.

Feel free to ask questions.