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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.
03B45 Modal logic (including the logic of norms)
03F40 Gödel numberings and issues of incompleteness
03F30 First-order arithmetic and fragments
Full Text: DOI
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