# AN ESCAPE FROM VARDANYAN’S THEOREM

@article{DEALMEIDABORGES2021ANEF, title={AN ESCAPE FROM VARDANYAN’S THEOREM}, author={Ana DE ALMEIDA BORGES and Joost J. Joosten}, journal={The Journal of Symbolic Logic}, year={2021} }

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…

## One Citation

### Towards a Coq formalization of a quantified modal logic

- Computer ScienceArXiv
- 2022

A Coq formalization of the Quantiﬁed Reﬂection Calculus with one modality, or QRC 1, focuses on the design decisions inherent to the formalization and the insights that led to new and simplifying proofs.

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