 During the next two decades or so after his first paper on basic logic, Fitch published a series of papers on basic logic devoted to (1) the representation of recursive functions (i.e., a demonstration of the possibility of the arithmetization of syntax), (2) \(K^\prime\), an extension of \(K\) with negation, universal quantifier and # (the dual of the \(*\) operator), (3) the consistency of \(K\) and \(K^\prime\), (4) \(L\), an extension of \(K^\prime\) with implication and necessity operators, (5) the definability of some of the constants such as \(*\) and #, as well as \(E\).