Horsetail, puzzlegrass, snakegrass / Best way to get rid of it?

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5 year old buck +
So, I guess I need to get a tractor in and dig a bit to drain the plot better.

But what chemicals/methods are best for erradicating/controlling it?
 
Horsetail? Lime. I spread heavy under my oaks and it knocked it right out. Took the ferns with it too.

horsetail.jpg
 
I've heard before that any chemical it would take to kill it would prevent you from growing a crop on it in the foreseeable future.
 
Will buckwheat grow if i lime heavily? Will buckwheat shade out the horsetail?
 
I would lime it heavily, then plant winter rye in it.
 
I would lime it heavily, then plant winter rye in it.

Will winter rye grow up between the snakegrass? I was thinking buckwheat in the Spring to shade it out. Maybe both?
 
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