There are various results in infinite combinatorics that are not usually considered "set theoretic combinatorics", such as
- Hindman's theorem
- Szemeredi's theroem
- The Carlson-Simpson theorem
- The Green-Tao theorem
I don't see any problem with labeling these "combinatorics", and I hope people are not removing the tag from them.
On the other hand, I would be suprised to find a question on Martin's axiom among questions tagged "combinatorics", but also (somewhat) surprised to find it among "infinitary combinatorics" questions. I would call it "set-theoretic combinatorics".
So I am not sure that just adding an "infinitary combinatorics" tag will resolve the situation. There are really at least three different classes of combinatorics questions, which I can roughly characterize by typical examples:
- Finite Ramsey's theorem / Four coloring theorem / Generating functions (finite combinatorics)
- Hindman's theorem / Szemeredi's theorem / Green-Tao Theorem (infinite combinatorics, but no set-theoretic issues)
- Martin's axiom / Jensen's diamond / Cardinal invariants of the continuum (infinite combinatorics with genuine set-theoretic issues)
Having two tags will force two of these to be lumped together. I would prefer to combine the first two rather than 2 and 3. There are also more difficult cases, such as the Erdos-Rado theorem.