Abstract

We shall dene a subhierarchy of the innitely deep languages N described by Jaakko Hintikka and Veikko Rentals see [1]). We shall show that some model theoretic results well-known in the model theory of the ordinary innitary language L can be generalized for these new language, too. In the innitely deep languages the denition of satisfaction is given by game theoretic means. The fact in N-formulas we allow `limit branches', i.e. branches the order type of which is a limit ordinal, brings about many unpleasant semantical features. One of these is the possibility of giving several dierent denitions of satisfaction. To avoid these inconveniences we restrict the original N { hierarchy by demanding that the order type of each branch in every formula tree is a successor ordinal. Thus we obtain a subhierarchy M, which much better suits our model theoretic consid- erations.