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  1. Strong and Weak Truth Principles.Bartosz Wcisło Mateusz Łełyk - 2017 - Studia Semiotyczne—English Supplement 29:107-126.
    This paper is an exposition of some recent results concerning various notions of strength and weakness of the concept of truth, both published or not. We try to systematically present these notions and their relationship to the current research on truth. We discuss the concept of the Tarski boundary between weak and strong theories of truth and we give an overview of non-conservativity results for the extensions of the basic compositional truth theory. Additionally, we present a natural strong theory of (...)
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  • Interpreting the Compositional Truth Predicate in Models of Arithmetic.Cezary Cieslinski - manuscript
    We present a construction of a truth class (an interpretation of a compositional truth predicate) in an arbitrary countable recursively saturated model of first-order arithmetic. The construction is fully classical in that it employs nothing more than the classical techniques of formal proof theory.
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  • Truth, Disjunction, and Induction.Ali Enayat & Fedor Pakhomov - 2019 - Archive for Mathematical Logic 58 (5-6):753-766.
    By a well-known result of Kotlarski et al., first-order Peano arithmetic \ can be conservatively extended to the theory \ of a truth predicate satisfying compositional axioms, i.e., axioms stating that the truth predicate is correct on atomic formulae and commutes with all the propositional connectives and quantifiers. This result motivates the general question of determining natural axioms concerning the truth predicate that can be added to \ while maintaining conservativity over \. Our main result shows that conservativity fails even (...)
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