Computability and Logic

This page contains scribbles and random musings as I process the contents of Computability and Logic. It’s not really for public consumption (unless you happen to care about my specific confusions).

Something that bugs me is that there is a classification of (partial) recursive(ly enumerable) sets, functions, etc. but textbooks seem to only state some of these results, rather than presenting a table with all the results visible at once.

Let \(f : \mathbf N \to \mathbf N\) be a partial or total function. If the {domain / range} of \(f\) is {recursively enumerable / enumerable in increasing order} then \(f\) is ____.

Let \(A \subset \mathbf N\) be a {recursive / recursively enumerable / recursively enumerable in increasing order} set. Then \(A\) can be the {domain / range} of a {recursive / partial recursive / primitive recursive} function.

Also there are multiple ways to pass between functions and sets here.