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It includes the study of Computability theory and Complexity theory.
In addition to their relevance to certain questions in the foundations of Set Theory (Ellentuck 1969), a leading application of combinatorial functions and operators has been to the branches of computability theory known as theory of recursive equivalence types (Myhill 1958) and isol theory (Nerode 1961; Dekker 1966); a fairly extensive survey of the latter area has been given in (McLaughlin 1982).
Acknowledging that there are deep issues involved,(10) standard practice in computability theory is to proceed on the assumption that the Church-Turing thesis is true, and to presume that results derived for Turing machines (or one of the other equivalent models of computation) apply to any realistic model of computation.