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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References found in this work BETA
Lev D. Beklemishev (1994). On Bimodal Logics of Provability. Annals of Pure and Applied Logic 68 (2):115-159.
V. Yu Shavrukov (1993). A Note on the Diagonalizable Algebras of PA and ZF. Annals of Pure and Applied Logic 61 (1-2):161-173.

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