Abstract
We present a model construction for the Calculus of Constructions (CC) where all dependencies are carried out in a set-theoretical setting. The Soundness Theorem is proved and as a consequence of it Strong Normalization for CC is obtained. Some other applications of our model constructions are: showing that CC + Classical logic is consistent (by constructing a model for it) and showing that the Axiom of Choice is not derivable in CC (by constructing a model in which the type that represents the Axiom of Choice is empty).KeywordsClassical LogicTypable TermStrong NormalizationDependent ProductSoundness TheoremThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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