Abstract
This chapter provides an overview the many-sorted version of calculus and the proof theoretic part of the Sort- Theorem. It presents a many-sorted version of a Hilbert-type calculus without function symbols and subsorts. The chapter presents a proof of soundness and completeness of the calculus and the model theoretic part of the Sort-Theorem. An alternative proof of the proof theoretic part of the Sort-Theorem is provided by an application of the Herbrand theorem. This proof was inadequate. The chapter presents a proof of a theorem that corresponds to the proof theoretic part of the Sort-Theorem.
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