 The following outline gives the flavor of an analogue of Gödel’s incompleteness theorem adapted to CL. It is possible to define a combinator such that if this combinator is applied to a numeral \(n\), then the whole term reduces to the numeral \(m\) that is the numeral denoting the Gödel number of the numeral \(n\). Slightly more formally, there is a combinator \(\delta\) such that \(\delta n = G(n)\) (where \(G (n)\) denotes the Gödel number of the expression \(n\)). Furthermore, there is a combinatory term, which returns the numeral itself followed by \(G(n)\), when applied to a numeral \(n\). For any term \(A\) there is a term \(B\) such that the equation \(A(\delta B)=B\) is true. This statement (or its concrete variant for a particular formal system) is usually called the second fixed point theorem. Computable characteristic functions of recursive sets of numbers can be represented by combinators with the choice of \(\textsf{K}\) for truth and \(\textsf{KI}\) for falsity. The complements of such functions are computable too. Finally, it can be proved that there is no combinator that represents the set of all true equations. To put it differently, any combinator either represents a set of equations that fails to include some true equations, or represents a set of equations that includes all true but also some false equations.