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I'm sorry to hear about your situation. Unfortunately, no, unless there's some HOA / local ordnance that specifically requires him to cut the tree in such a situation. Otherwise, there's nothing that you could do to make him cut his tree that is on his property, even though branches are extending onto your property. It's true that you have the right to trim the branches to the property line, but not further.
Jones v. Wagner, 624 A.2d 166 (1993), appeal denied, 536 Pa. 626 (1993). It generally is understood that an owner of realty has a cause of action against any person who has committed a trespass upon his land. What is less generally known is that this cause of action does not require that the landowner allege any actual injury or damage. The harm that is to be remedied is the right to peaceably enjoy full, exclusive use of the property, not the fact that the property is being damaged. Moreover, a landowner generally has a right not only to the exclusive possession of the surface of his property but also to what lies above and below it. There is a property right in the air space above the land, and this property right can be invaded by overhanging objects, including tree limbs. When tree branches overhang a property line, the aggrieved landowner is not limited to seeking monetary relief for any damage that may have occurred. When tree limbs grow over onto another person’s property, there is a trespass. In fact, in the case of tree limbs, there is a continuing trespass occurring by the mere fact of the overhang and the possessor of land is entitled to pursue various remedies, including self-help. With regard to self-help, an aggrieved landowner is entitled to trim the branches back to the property line, and this is true even if the overhanging branches do not damage the property. Also, if the landowner has incurred reasonable expenses in the course of exercising a self-help remedy, he may recoup those expenses from the trespasser.
So while it's expensive, this case holds that you have the right to go after him for reasonable expenses in exercising your self-help remedy. You can't force him to remove it unless it poses an unreasonable risk of harm to your property, but you can seek repayment from him. If he doesn't pay, you can take him to small claims court and use this case as support for your claim against him.
Hope that clears things up a bit. If you have any other questions, please let me know. If not, and you have not yet, please rate my answer AND press the "submit" button, if applicable. Please note that I don't get any credit for the time and effort that I spent on this answer unless and until you rate it positively (3 or more stars). Look for the stars on your screen (★★★★★). Thank you, ***** ***** luck to you!