Select saute setting on a 6-qt. electric pressure cooker. Adjust for medium heat; add oil.
Add tomatoes, onion and garlic to drippings; cook and stir until crisp-tender, 3-5 minutes, mashing tomatoes lightly.
Cook, covered, on low until ribs are tender, 6-8 hours. Remove ribs; shred with 2 forks and serve with reserved cooking juices.