Infinitary logic and basically disconnected compact Hausdorff spaces

Antonio Di Nola; Serafina Lapenta; Ioana Leustean

doi:10.1093/logcom/exy011

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arXiv · 1709.08397

Infinitary logic and basically disconnected compact Hausdorff spaces

Antonio Di Nola·Serafina Lapenta·Ioana Leustean

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Abstract

We extend \L ukasiewicz logic obtaining the infinitary logic $\mathcal{IR}\L$ whose models are algebras $C(X,[0,1])$, where $X$ is a basically disconnected compact Hausdorff space. Equivalently, our models are unit intervals in $\sigma$-complete Riesz spaces with strong unit. The Lindenbaum-Tarski algebra of $\mathcal{IR}\L$ is, up to isomorphism, an algebra of $[0,1]$-valued Borel functions. Finally, our system enjoys standard completeness with respect to the real interval $[0,1]$.

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BibTeX RIS

Antonio Di Nola, Serafina Lapenta, Ioana Leustean. 2017-09-25. Infinitary logic and basically disconnected compact Hausdorff spaces. https://doi.org/10.1093/logcom/exy011

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