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The logic of linear tolerance

Studia Logica 51 (2):249 - 277 (1992)

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  1. Essential hereditary undecidability.Albert Visser - 2024 - Archive for Mathematical Logic 63 (5):529-562.
    In this paper we study essential hereditary undecidability. Theories with this property are a convenient tool to prove undecidability of other theories. The paper develops the basic facts concerning essentially hereditary undecidability and provides salient examples, like a construction of essentially hereditarily undecidable theories due to Hanf and an example of a rather natural essentially hereditarily undecidable theory strictly below. We discuss the (non-)interaction of essential hereditary undecidability with recursive boolean isomorphism. We develop a reduction relation essential tolerance, or, in (...)
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  • Undecidability in diagonalizable algebras.V. Shavrukov - 1997 - Journal of Symbolic Logic 62 (1):79-116.
    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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  • A Simple Proof of Arithmetical Completeness for $\Pi_1$ -Conservativity Logic.Giorgi Japaridze - 1994 - Notre Dame Journal of Formal Logic 35 (3):346-354.
    Hájek and Montagna proved that the modal propositional logic ILM is the logic of -conservativity over sound theories containing I (PA with induction restricted to formulas). I give a simpler proof of the same fact.
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