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Incompleteness and fixed points. (English) Zbl 0988.03037
Summary: Our purpose is to present some connections between modal incompleteness and modal logics related to the Gödel-Löb logic GL. One of our goals is to prove that for all \(m,n,k,l \in\mathbb{N}\) the logic \(\text{K}+\bigwedge_{i=m}^n \square^i (\bigwedge^l_{j=k} \square^j p\leftrightarrow p)\to \bigwedge^n_{i=m} \square^ip\) 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.
MSC:
03B45 Modal logic (including the logic of norms)
03F40 Gödel numberings and issues of incompleteness
03F30 First-order arithmetic and fragments
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