Abstract
We define a subhierarchy of the infinitely deep languagesN ℵλ described by Jaakko Hintikka and Veikko Rantala. We shall show that some model theoretic results well-known in the model theory of the ordinary infinitary languages ℒℵλ can be generalized for these new languages. Among these are the downward Löwenheim-Skolem and Łoś's theorems as well as some compactness properties.
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Karttunen, M. Model theoretic results for infinitely deep languages. Stud Logica 42, 223–241 (1983). https://doi.org/10.1007/BF01063842
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DOI: https://doi.org/10.1007/BF01063842