author={Ana DE ALMEIDA BORGES and Joost J. Joosten},
  journal={The Journal of Symbolic Logic},
Vardanyan’s Theorems [36, 37] state that QPLpPAq – the quantified provability logic of Peano Arithmetic – is Π02 complete, and in particular that this already holds when the language is restricted to a single unary predicate. Moreover, Visser and de Jonge [38] generalized this result to conclude that it is impossible to computably axiomatize the quantified provability logic of a wide class of theories. However, the proof of this fact cannot be performed in a strictly positive signature. The… 

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