More on monadic logic. C: Monadically interpreting in stable unsuperstable \(\mathcal T\) and the monadic theory of \(^{\omega}\lambda\) (Q916645)

[For Parts A and B see ibid. 63, No. 3, 335--352 (1988; Zbl 0664.03034) and ibid. 69, No. 1, 94--116 (1990; Zbl 0698.03034), respectively.] This paper contributes to the classification of pairs (\(\mathcal T,Q)\) where \(\mathcal T\) is a first order theory and \(Q\) is a quantifier. The main result concerns \(\mathcal T\) in a finite language which are stable but not superstable. For such \(\mathcal T\) ``one can, in monadic logic, interpret in it essentially trees \((^{\omega \geq}\lambda,<)\) with quantification \((Q^{pd}f)\) (on pressing down functions)''. Knowledge of earlier papers is required of the reader.