Infinitary logic and basically disconnected compact Hausdorff spaces

Antonio Di Nola, Serafina Lapenta, Ioana Leustean

We extend Łukasiewicz logic obtaining the infinitary logic $\mathcal{I}\mathcal{R}Ł$ whose models are algebras $C(X,[0,1])$, where $X$ is a basically disconnected compact Hausdorff space. Eq…