Kleene's Two Kinds of Recursion

@article{Kavvos2016KleenesTK,
  title={Kleene's Two Kinds of Recursion},
  author={G. A. Kavvos},
  journal={CoRR},
  year={2016},
  volume={abs/1602.06220}
}
This is an elementary expository article regarding the appl ication of Kleene’s Recursion Theorems in making definitions by recursion. Wherea s the Second Recursion Theorem (SRT) is applicable in a first-order setting, the First Recur sion Theorem (FRT) requires a higherorder setting. In some cases both theorems are applicable, b ut one is stronger than the other: the FRT always produces least fixed points, but this is not always the case with the SRT. Nevertheless, an old result by Rogers… CONTINUE READING