World travelling and mood swings

In Benedikt Löwe, Thoralf Räsch & Wolfgang Malzkorn (eds.), Foundations of the Formal Sciences II. Kluwer (2003)
It is not quite as easy to see that there is in fact no formula of this modal language having the same truth conditions (in terms of S5 Kripke semantics) as (1). This was rst conjectured by Allen Hazen2 and later proved by Harold Hodes3. We present a simple direct proof of this result and discuss some consequences for the logical analysis of ordinary modal discourse.
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Kai Frederick Wehmeier (2004). In the Mood. Journal of Philosophical Logic 33 (6):607-630.
Alexander W. Kocurek (2016). The Problem of Cross-World Predication. Journal of Philosophical Logic 45 (6):697-742.
Jordan Stein (2013). How Many Notions of Necessity? Philosophical Studies 165 (2):605-627.

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