Classical Computability - Preliminaries and Notation

Here's everything concerning notation, abbreviations, definitions used in this text about classical computability theory, including some basic presupposed results: Preliminaries and Notation in pdf.
Note that the schemes of Composition (CN) and Primitive Recursion (PR) are defined for partial (not necessarily total) number-theoretic functions from the outset and therefore might look significantly different to what one finds in computability textbooks.