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I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear about your situation.
In a divorce, each spouse is entitled to half the equity in the marital home. This is true regardless of who paid for what during the marriage. If you can afford to buy out your wife's share, then the judge will most likely allow you to keep the property, as long as you can continue to make the payments. She cannot force you to sell the house without a court order, though, and to get a court order, she needs to convince the divorce court judge that it's fair for you to have to sell the house.
The judge can order you to make reasonable efforts to refinance the house in your name only, but even if you can't, you may be able to stay as long as you can make the payments.
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