Incompleteness and Fixed Points

Mathematical Logic Quarterly 48 (1):15-28 (2002)

Abstract

Our purpose is to present some connections between modal incompleteness andmodal logics related to the Gödel-Löb logic GL. One of our goals is to prove that for all m, n, k, l ∈ ℕ the logic K + equation image□i □jp ↔ p) → equation image□ip is incomplete and does not have the fixed point property. As a consequence we shall obtain that the Boolos logic KH does not have the fixed point property

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References found in this work

An Incomplete System of Modal Logic.George Boolos & Giovanni Sambin - 1985 - Journal of Philosophical Logic 14 (4):351 - 358.
Magari's Theorem Via the Recession Frame.M. J. Cresswell - 1987 - Journal of Philosophical Logic 16 (1):13 - 15.
Some Descending Chains of Incomplete Modal Logics.Ming Xu - 1991 - Journal of Philosophical Logic 20 (3):265 - 283.

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