 Monotonicity ensures (in set theory) that one finds an ordinal \(\tau\) such that \(\Gamma(\Gamma^{\tau})=\Gamma^{\tau}\), and the set \(\Gamma^{\tau}\) will be the least fixed point. If one adds a new 1-place predicate symbol P to the language of arithmetic, one can describe the so-called positive arithmetical operators. They are of the form 