The succinctness of first-order logic over modal logic via a formula size game

In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. CSLI Publications. pp. 491-419 (2016)
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Modal Logic.Marcus Kracht - 2002 - Bulletin of Symbolic Logic 8 (2):299-301.
Multi-dimensional modal logic.Maarten Marx - 1997 - Boston, Mass.: Kluwer Academic Publishers. Edited by Yde Venema.
Multi-Dimensional Modal Logic.Maarten Marx & Yde Venema - 2000 - Studia Logica 65 (2):278-282.
Some Exponential Lower Bounds on Formula-size in Modal Logic.Hans van Ditmarsch, Wiebe van der Hoek & Petar Iliev - 2014 - In Rajeev Goré, Barteld Kooi & Agi Kurucz (eds.), Advances in Modal Logic, Volume 10. CSLI Publications. pp. 139-157.

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