A cut-free calculus for second-order Gödel logic

Abstract We prove that the extension of the known hypersequent calculus for standard first-order Godel logic with usual rules for second-order quantifiers is sound and (cut-free) complete for Henkin-style semantics for second-order Godel logic. The proof is semantic, and it is similar in nature to Schutte and Tait's proof of Takeuti's conjecture.

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