@article{d6d0c19f38dc41b096afe6ee03085421,
title = "A note on humberstone{\textquoteright}s constant Ω",
abstract = "We investigate an expansion of positive intuitionistic logic obtained by adding a constant Ω introduced by Lloyd Humberstone. Our main results include a sound and strongly complete axiomatization, some comparisons to other expansions of intuitionistic logic obtained by adding actuality and empirical negation, and an algebraic semantics. We also briefly discuss its connection to classical logic.",
keywords = "Actuality operator, And phrases: intuitionistic logic, Deduction theorem, Empirical negation, Minimal logic",
author = "Satoru Niki and Hitoshi Omori",
note = "Funding Information: We would like to thank Lloyd Humberstone for directing our attention to his paper [8] after an online presentation by S.N. of our [13] in August, 2020 at Advances in Modal Logic 2020. S.N. would also like to thank Hiroakira Ono for his helpful comments on the algebraic semantics. Moreover, we would like to thank Michael De for this helpful comments on an earlier version. Finally, but not the least, we would like to thank the anonymous referee for an extremely detailed, encouraging, and helpful report with a number of comments, corrections, and suggestions. The research of H.O. was supported by a Sofja Kovalevskaja Award of the Alexander von Humboldt-Foundation, funded by the German Ministry for Education and Research. Moreover, for the preparation of the revised version of this note, S.N. was also supported by a Sofja Kovalevskaja Award of the Alexander von Humboldt-Foundation, funded by the German Ministry for Education and Research. Publisher Copyright: {\textcopyright} 2021 Jagiellonian University Press. All rights reserved.",
year = "2021",
doi = "10.4467/20842589RM.21.004.14376",
language = "English",
volume = "56",
pages = "75--99",
journal = "Reports on Mathematical Logic",
issn = "0137-2904",
publisher = "Jagiellonian University Press",
}