Abstract
We prove that all proofs in ω-logic (a first order logic with ω-rule added) in which ω-rule is used finitely many times can be turned into proofs in which the ω-rule is used at most one time. Next, we prove that the word “finitely” above cannot be changed by the word “infinitely”.
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References
H. Leblanc, P. Roeper, M. Thau, G. Weaver, Henkin's Completeness Proof: Forty Years Later, The Notre Dame Journal of Formal Logic, forthcoming.
F. B. Fitch, Intuitionistic Modal Logic With Quantifiers Portugaliae Mathematica 17 (1948), pp. 113–119.
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Thau, M. The ω-rule. Stud Logica 51, 241–248 (1992). https://doi.org/10.1007/BF00370115
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DOI: https://doi.org/10.1007/BF00370115