I don't know who told you you can't have heavy cream on Induction, but it is perfectly legal. Don't go overboard, limit yourself to 2 or 3 tablespoons a day. It's very high in calories and fat, which is actually good for you. And count each ounce as 1 carb. It's not enough for them to list it on the label — USDA says anything up to .9 carbs per serving can be listed as "0" — but there are some carbs.

By the way — some heavy cream whipped up with Splenda is a great dessert! It's delicious on SF Jello and, later, on berries.