Undecidability in diagonalizable algebras

Journal of Symbolic Logic 62 (1):79-116 (1997)
If a formal theory T is able to reason about its own syntax, then the diagonalizable algebra of T is defined as its Lindenbaum sentence algebra endowed with a unary operator □ which sends a sentence φ to the sentence □φ asserting the provability of φ in T. We prove that the first order theories of diagonalizable algebras of a wide class of theories are undecidable and establish some related results
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DOI 10.2307/2275733
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On Bimodal Logics of Provability.Lev D. Beklemishev - 1994 - Annals of Pure and Applied Logic 68 (2):115-159.
On Propositional Quantifiers in Provability Logic.Sergei N. Artemov & Lev D. Beklemishev - 1993 - Notre Dame Journal of Formal Logic 34 (3):401-419.

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