The Disjunction and Existence Properties for Axiomatic Systems of Truth

Annals of Pure and Applied Logic 40 (1):1--10 (1988)
In a language for arithmetic with a predicate T , intended to mean “ x is the Gödel number of a true sentence”, a set S of axioms and rules of inference has the truth disjunction property if whenever S ⊢ T ∨ T , either S ⊢ T or S ⊢ T . Similarly, S has the truth existence property if whenever S ⊢ ∃χ T ), there is some n such that S ⊢ T ). Continuing previous work, we establish whether these properties hold or fail for a large collection of possible axiomatic systems
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Volker Halbach, Axiomatic Theories of Truth. Stanford Encyclopedia of Philosophy.

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