On the proof-theory of two formalisations of modal first-order logic

Studia Logica 96 (3):349-373 (2010)
We introduce a Gentzen-style modal predicate logic and prove the cut-elimination theorem for it. This sequent calculus of cut-free proofs is chosen as a proxy to develop the proof-theory of the logics introduced in [14, 15, 4]. We present syntactic proofs for all the metatheoretical results that were proved model-theoretically in loc. cit. and moreover prove that the form of weak reflection proved in these papers is as strong as possible
Keywords Gentzen-style logic  Hilbert-style logic  modal first-order logic  sequent calculus  cut-elimination  reflection theorem
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