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That is possible. Normally this would be negotiated out of court, but otherwise you can take it to court and the court will appreciate your seeking to remedy the problem and likely punish landlord for not curing this dangerous condition. The court date can get postponed which is not uncommon but you may seek a date convenient for you.
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feel free to follow up with me. I can send you an offer to review documents after you rate my answer. Kindly rate me positively.