# metadata.dc.description.abstract[].value
Vardanyan’s Theorems [36, 37] state that QPL(PA)—the quantified provability logic of
Peano Arithmetic—isΠ02
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 system QRC1 was previously
introduced by the authors [1] as a candidate first-order provability logic. Here we generalize the previously
available Kripke soundness and completeness proofs, obtaining constant domain completeness. Then we
show that QRC1 is indeed complete with respect to arithmetical semantics. This is achieved via a Solovaytype
construction applied to constant domain Kripke models. As corollaries, we see that QRC1 is the
strictly positive fragment of QGL and a fragment of QPL(PA).

# metadata.dc.rights[].value
cc-by (c) Borges, Ana de Almeida Gabriel Vieira et al, 2023

# metadata.dc.source[].value
Articles publicats en revistes (Filosofia)