In a 5 to 6-quart slow cooker, combine the carrots, celery, onion, potatoes and thyme. Place the corned beef, fat-side-up, on top of the vegetables; sprinkle with pickling spice. Pour in the water (or more—enough to almost cover the meat). Cover and cook on high until the corned beef is tender (4 hours + 15 minutes). Arrange the cabbage over the corned beef, cover and continue cooking on high until the cabbage is tender, 45 minutes.