Cut the cabbage into quarters and remove the core. Shred the cabbage as finely as possible and transfer to a large bowl. Using the coarsest side of a box grater, shred the carrots; halve the green pepper and remove the seeds, ribs, and stem, then cut them into extremely fine strands; cut the celery thin and crosswise and add all ingredients to the cabbage.
To make the dressing, whisk together the vinegar, oil, sugar, salt, and pepper in a small bowl. Pour the dressing over the slaw. Toss well.
Refrigerate the slaw, tightly covered, for at least 8 hours before serving. As the slaw will not wilt much, it should remain crisp and fresh tasting for 2 to 3 weeks.