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computable sets and functions, Turing degrees, c.e. degrees, models of computability, primitive recursion, oracle computation, models of computability, decision problems, undecidability, Turing jump, halting problem, notions of computable randomness, computable model theory, computable equivalence relation theory, arithmetic and hyperarithmetic hierarchy, infinitary computability, $\alpha$-recursion, complexity theory.
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Is it correct to state that basic primitive recursive functions are in fact combinators?
Yes, if I'm right in assuming you mean to ask whether these can be construed without free variables in the lambda calculus. (If my assumption is wrong, I apologize; your question is rather terse.) Y …