PRESIDENT REAGAN has achieved a great deal in the provisional agreement with the Soviets on nuclear arms questions announced over the past few days. The agreement to eliminate intermediate- and short-range nuclear forces marks an arms-control first for him, and it both reflects and vindicates the president's determination to reduce and not just manage numbers of weapons; it also brings the prospect of an autumn summit. Especially after the Reykjavik debacle, he will be obliged to demonstrate that he has not bought a dubious accord. But if he cannot do so, the accord won't be worth much anyway.

The achievement brings other obligations, mainly to confront the range of difficulties that an INF agreement and the intensifying diplomatic exchanges point up. In Europe, for example, the welcome widely accorded to this great-power accommodation is tempered with wariness that the United States may be reducing its European commitment and with doubts that Europeans can make the necessary compensation for the nuclear weapons to be removed -- compensation in conventional arms and in general defense cooperation. One way, of course, would be the leveling of the Soviets' current and ominous advantage in conventional attack capability. Organizing the negotiations to bring this about will be real work.

There is also the job of making good on the mutual and now-freshened Soviet-American commitment to cut strategic offensive arsenals by half. Here the threshold issue is how offensive cuts are to relate to nuclear defense, and three critical battles are raging:

One pits Moscow's insistence on linking offensive-weapons cuts to limits on the American Strategic Defense Initiative against Washington's resistance to such linkage.

A second pits the administration's defense of this position against a Democratic-controlled Congress' threat to use its power of the purse to legislate some of the "Star Wars" restrictions that the president has so far refused to accept.

A third -- which the president still has not resolved -- pits Secretary of State Shultz against Secretary of Defense Weinberger in a battle over the president's own position. Mr. Shultz is looking for a way to combine offensive cuts and continuation of work on SDI; Mr. Weinberger's priority is to accelerate progress on SDI and to keep arms control from getting in the way.

What is the way out for Mr. Reagan? Above all, he needs finally to decide what he wants and to resolve the longstanding Shultz-Weinberger dispute. That's what presidents are supposed to do. The Shultz course is better. It would let the president continue a robust SDI program. It would help him get Congress off his back, since most of the Democrats have a much greater difference with Mr. Weinberger than they do with Mr. Shultz. It would give him a position that not only serves the American interest but appears to offer a good basis for negotiation with the Russians.

There is an excitement to the progress on INF. At the same time, warnings of euphoria are heard. The warnings are useful. In the 1970s, feeling outran reality -- especially the reality of Soviet-American global rivalry -- and everybody paid. This is why President Reagan is entirely right to put the emphasis he does on easing regional disputes and also on persuading the Kremlin to better equip itself for international partnership by treating its citizens with dignity.

At the same time, the special destructive quality of nuclear weapons puts a special burden on those who possess them to miss no opening to make the world more secure. President Reagan and General Secretary Gorbachev have created an unusual opportunity to pursue this great goal.