Successor ordinals are ordinals that immediately follow a given ordinal, representing the next step in the well-ordered sequence of ordinals. They are crucial for understanding the construction of ordinal numbers, as each successor ordinal is formed by adding one to a given ordinal, distinguishing them from limit ordinals which are not preceded by any single ordinal.
The Recursion Theorem in computer science and mathematics states that for any computable function, there exists a program that can reproduce its own source code as output. This theorem underpins the concept of self-replicating programs and is fundamental to understanding the limits of computation and the nature of algorithms that can manipulate their own structure.