Infinitary logic and basically disconnected compact Hausdorff spaces
Antonio Di Nola, Serafina Lapenta, Ioana Leuştean · Journal of Logic and Computation · 2018
We extend Łukasiewicz logic obtaining the infinitary logic Infinitary Riesz Logic (|$\mathcal{IR}$|Ł) whose models are algebras C(X, [0, 1]), where X is a basically disconnected compact Hausdorff space. Equivalently, our models are unit intervals in Dedekind |$\sigma $|-complete Riesz spaces with strong unit. The Lindenbaum–Tarski algebra of |$\mathcal{IR}$|Ł is, up to isomorphism, an algebra of [0, 1]-valued Borel functions. Finally, our system enjoys standard completeness with respect to the real interval [0, 1].