Kleene's Two Kinds of Recursion [article]

G. A. Kavvos
2018 arXiv   pre-print
This is an elementary expository article regarding the application of Kleene's Recursion Theorems in making definitions by recursion. Whereas the Second Recursion Theorem (SRT) is applicable in a first-order setting, the First Recursion Theorem (FRT) requires a higher-order setting. In some cases both theorems are applicable, but 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 allows
more » ... s to bridge this gap by subtly redefining the implementation of a higher-order functional in order to bring it to a 'standard form.'
arXiv:1602.06220v2 fatcat:fyy2vtj43zb7xk7x7dtqdkl2mq