Hard Provability Logics

Mojtaba Mojtahedi

Let $\mathcal{P}\mathcal{L}(\mathsf{T},{\mathsf{T}}^{\prime })$ and ${\mathcal{P}\mathcal{L}}_{{\Sigma }_1}(\mathsf{T},{\mathsf{T}}^{\prime })$ respectively indicates the provability logic and ${\Sigma }_1$-provability logic of $\mathsf{T}$ relative in ${…