In a large pot over high heat, combine the pork, salt and water to cover. Bring to a boil and reduce heat to medium low. Allow to simmer for two hours, skimming foam as necessary.
Remove from heat and take the bones out of the stock. Cool and de-fat the stock. Remove pork from bones and return meat to stock. Add the hominy and chili powder and simmer over low heat for 30 to 45 minutes.
Serve by placing soup in bowls. Each diner then adds their own cabbage, radishes, onion and lime juice to taste. Eat by dipping spoon deep down to bottom of bowl, lifting to bring up the meat, hominy, soup and layered vegetables.