I survey the syntactic technique of tiering which can be used to restrict the power of a recursion scheme. I show how various results can be obtained entirely proof theoretically without the use of a model of computation.
Harold Simmons. "Tiering as a recursion technique." Bull. Symbolic Logic 11 (3) 321 - 350, September 2005. https://doi.org/10.2178/bsl/1122038991