Removing ivy from a tree

We have a massive oak tree in the front yard, and the ivy (English) that covers the ground under it has grown up onto the tree. We recently bought the house, and I'd guess this has been going on for 10 years--the ivy is at least 25 feet up the trunk, and well-established.
I want to remove the ivy from the tree, so about 2 months ago I cut all of the vines on the base of the tree--basically created a "clear cut" circle about 1 foot up the trunk. cut off from the ground I expected the ivy on the tree to cooperate by dying out, and then I'd pull the dead vines off of the tree.
Right.
The ivy on the tree seems to be as healthy as ever. Is that a surprise? Can it live without access to the ground? Does that mean it's getting water/nutrients directly from the tree?
How should I go about removing/killing the ivy from the tree? I'm not opposed to applying Roundup or something similar, if I can do so w/o harming the tree.
Any recommendations would be appreciated.
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As long as we are talking about a fairly large tree, which if it is covered in ivy it probably is, then you can spray roundup on the ivy leaves without harming the tree. If it is at the base of the tree where there are no limbs or tree leaves you should have no problem. Roundup is absorbed in the green foliage and then travels to the plant roots and kills the plant. I would try to keep it off the tree leaves but it would take a tremendous amout of Roundup to harm a large oak, assuming the trunk is many feet in diameter, not a young tree with a 6" diameter trunk. The ivy above the cut you made will eventually die on its own. Since the weather is now so cool it can survive quite some time cut off from the root system. Some Roundup on the green leafy parts will hasten it's demise. One thing you need to know about Roundup, it works best when the plant is in its active growing season in the warmer months when it is actively exchanging water and nutrients between the leaves and the root system. In the late fall and winter this process can slow dramatically as the temperatures drop and it can take a long time for the Roundup to take effect. Once you get into freezing weather Roundup generally works poorly if at all. In essence the tranport system in the plant has slowed to a crawl or shutdown entirely and the leaves will not take up the material before it gets washed off. Conversely, if you run into protracted hot dry weather in the summer Roundup can loose it effectiveness since most plants will try to shutdown and go dormant to ride out the dry spell. Spring, early summer and early fall are the best times to use Roundup type herbicides.
Rich wrote:

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Thank you. That's exactly the sort of info I was after--very helpful.

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