If your wife took out credit cards in your name without your consent, you have the option to contact the credit card company and file an affidavit with them swearing that the accounts were fraudulently opened in your name without your consent, at which point the credit card companies will not hold you liable. Also, it sounds like you're still in mediation. Certainly the divorce court has the authority to assign debts to either party, regardless of whose name they're in. Remember, however, that the court cannot absolve you of liability toward a third-party creditor for debts held individually or jointly in your name, or with you as co-signer, so it is important in the divorce decree to get language providing that your spouse must "indemnify" you and hold you harmless from any debts assigned to her, for which you remain liable to the third-party creditor, including the cost of attorney's fees necessary to enforce the indemnification clause. Here is an article I've written on the subjection of asset and debt allocation in MN divorce, which includes a section on debt treatment: http://www.minnesotadivorce.com/articles/property-and-debt-allocation/index.html
First, you do not indicate whether any court orders have been entered in your case. A mediated agreement must be memorialized as a court order before it become binding and/or enforceable.
Second, a court may divided debts equitably. That means in a way that the Judge deems to be fair. That may mean requiring one party to pay to another a lump sum. It may mean awarding to one party who takes on more of the debt a greatedr amount of the assets. It may mean refinancing the debt where that is possible. If youmediating the issue, all of those considerationshould be included in your discussions and as part of any subsequent court order. If it is excluded from the court order, there is nothing you can do to repair the issue.
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Because you use the term "ex-wife", I will presume that you have already been divorced. If as part of a divorce decree responsibility for a specific debt item was assigned to her, I do hope that there was language in the decree through which she must indemnify you against any obigation for such debt. Of course, if a creditor is now going after you for such an item, you may have to bring your ex back to court on a contempt action to really hold her feet to the metaphorical fire. One of the difficult things about allocation of debts in a marriage dissolution is that creditors are not a party to your divorce. Therefore, you are still "live meat" for them to go after to satisfy the debt owed. Your remedy is most likely to go back after your ex for what sounds like contempt of the divorce decree. If she is found in contempt, the Court has many options; it can order her to pay the debts and potentially your attorney fees as well (among other things).
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