Norwegian, like Swedish and Faroese, exhibits double definiteness: modified definite phrases normally contain both a prenominal determiner and a suffixed definite article on the noun. However, exceptions—phrases with only the determiner or only the suffixed article—can be found. This article investigates adjectives which do not need to be preceded by the prenominal determiner in Norwegian. Corpus data and acceptability judgments are used to describe these exceptions and to propose a syntactic analysis. The study shows that there are three types of adjectives in Norwegian: regular ones that require double definiteness, exceptional adjectives that allow determiner omission, and quantifier adjectives that never occur with a determiner. I argue that phrases with exceptional adjectives can be accounted for by the same movement that is proposed for determiner-less phrases in Icelandic and Northern Swedish (Julien 2002, 2005). Finally, the article presents a brief exploration of the patterns of variation in omission versus presence of the determiner, including historical and dialectal variation.

We formalize in Constructive Type Theory the Lambda Calculus in its classical first-order syntax, employing only one sort of names for both bound and free variables, and with α-conversion based upon name swapping. As a fundamental part of the formalization, we introduce principles of induction and recursion on terms which provide a framework for reproducing the use of the Barendregt Variable Convention as in pen-and-paper proofs within the rigorous formal setting of a proof assistant. The principles in question are all formally derivable from the simple principle of structural induction/recursion on concrete terms. We work out applications to some fundamental meta-theoretical results, such as the Church–Rosser Theorem and Weak Normalization for the Simply Typed Lambda Calculus. The whole development has been machine checked using the system Agda.