Model theoretic results for infinitely deep languages (Q1060213)

We define a subhierarchy of the infinitely deep languages \({\mathcal N}_{\kappa \lambda}\) described by \textit{J. Hintikka} and \textit{V. Rantala} [Ann. Math. Logic. 10, 95-115 (1976; Zbl 0339.02013)]. We shall show that some model theoretic results well-known in the model theory of the ordinary infinitary languages \({\mathcal L}_{\kappa \lambda}\) can be generalized for these new languages. Among these are the downward Löwenheim-Skolem and Łosś theorems as well as some compactness properties.