The doctor's association has threatened to go on indefinite strike to support/in support of/in support for their teachers.
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closed as not a real question by waiwai933♦ Jan 14 '13 at 8:10
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Both in support of and to support are correct.
Kelly was correct in that to support implies direct help--as if the strike will directly cause a change in the doctor's assocation.
In support of implies indirect help--the doctor's association is threatening to go on strike for moral support. The strike itself may not do much, but it's a statement--the doctor's assocation cares about their teachers.
Both "to support" and "in support of" are grammatically correct. "To support" has a slightly stronger connotation of direct help, while "in support of" could suggest moral support or making a statement. That's a very slight and subtle difference though, and a lot of people might not make that distinction.
I don't think "in support for" is idiomatic. It doesn't seem to be used this way. (A Google search shows that "in support for" mostly comes up in phrases like "a drop in support for X," which means the amount of support dropped, not that something was dropped to support X.)
So, either "to support" and "in support of" is fine. If you want to distinguish between direct help and moral support, I suggest "to support" for more direct help and "in support of" for moral support.
First of all prepositions are a bit tricky in English. In most cases the use of prepositions depend on the context; hence, there are no strict rules governing the use of prepositions. To answer your question, here is my take on it.
To support is the infinitive form of the verb support and could mean provide for, help, hold up, back up, back, advocate or promote, etc. Here are a few examples:
Now according to OED and NOAD, in support of is a phrase and means:
In support for means roughly the same as in support of in your example. Here are a few examples:
That said, in your example all three are grammatical and mean roughly the same thing. I would use in support of not because it's the best fit, but it feels better in the context at issue.