Abstract
We investigate the Friedman–Goldfarb–Harrington theorem from two perspectives. Firstly, in the frameworks of classical and modal propositional logics, we study the forms of sentences whose existence is guaranteed by the FGH theorem. Secondly, we prove some variations of the FGH theorem with respect to Rosser provability predicates.
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Acknowledgements
This work was partly supported by JSPS KAKENHI Grant Number JP19K14586. The author would like to thank Sohei Iwata, Haruka Kogure, and Yuya Okawa for their helpful comments. The author would also like to thank the anonymous referees for their valuable comments and suggestions. In particular, the current proofs of Theorems 1 and 2 using Lemmas 1 and 2 are based on the ideas of one of the referees, which made the proofs significantly simpler and easier to understand.
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Presented by Yde Venema; Received October 28, 2021.
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Kurahashi, T. Some Observations on the FGH Theorem. Stud Logica 111, 749–778 (2023). https://doi.org/10.1007/s11225-023-10045-6
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DOI: https://doi.org/10.1007/s11225-023-10045-6