Reduction of provability logics to Σ1-provability logics
Mohammad Ardeshir, Mojtaba Mojtahedi · Logic Journal of IGPL · 2015
We show that the provability logic of PA, GL and the truth provability logic, i.e. the provability logic of PA relative to the standard model ℕ, GLS are reducible to their Σ1-provability logics, GLV and GLSV, respectively, by only propositional substitutions.