Topic summary
Cut-elimination
Extracted from the Wikipedia article Cut-elimination theorem.
There are many different possible sequent calculuses for many logics, and consequently there are many different cut-elimination theorems. Indeed, cut-elimination is such an important genre of theorems in logic, that logicians speak of "this logic has cut-elimination" as a way to say that this logic has a desirable property. Conversely, if a formalism or a logic does not have cut-elimination, that is usually considered a point against it, and would motivate research into finding a new formalism, or a modification of the logic, such that cut-elimination is true, or an analog of cut-elimination is true.