We extend Lukasiewicz logic obtaining the infinitary logic Infinitary Riesz Logic (IRL) 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 Ries[spaces with strong unit. The Lindenbaum-Tarski algebra of IRL 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].

Infinitary logic and basically disconnected compact Hausdorff spaces

Di Nola, Antonio;LAPENTA, SERAFINA
;
LEUSTEAN, IOANA GABRIELA
2018-01-01

Abstract

We extend Lukasiewicz logic obtaining the infinitary logic Infinitary Riesz Logic (IRL) 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 Ries[spaces with strong unit. The Lindenbaum-Tarski algebra of IRL 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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/4719741
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