In this article we investigate infinitary propositional logics from the perspective of their completeness properties in abstract algebraic logic. It is well-known that every finitary logic is complete with respect to its relatively (finitely) subdirectly irreducible models. We identify two syntactical notions formulated in terms of (completely) intersection-prime theories that follow from finitarity and are sufficient conditions for the aforementioned completeness properties. We construct all the necessary counterexamples to show that all these properties define pairwise different classes of logics. Consequently, we obtain a new hierarchy of logics going beyond the scope of finitarity.

Lavicka, T., Noguera, C. (2017). A New Hierarchy of Infinitary Logics in Abstract Algebraic Logic. STUDIA LOGICA, 105(3), 521-551 [10.1007/s11225-016-9699-3].

A New Hierarchy of Infinitary Logics in Abstract Algebraic Logic

Noguera C.
2017-01-01

Abstract

In this article we investigate infinitary propositional logics from the perspective of their completeness properties in abstract algebraic logic. It is well-known that every finitary logic is complete with respect to its relatively (finitely) subdirectly irreducible models. We identify two syntactical notions formulated in terms of (completely) intersection-prime theories that follow from finitarity and are sufficient conditions for the aforementioned completeness properties. We construct all the necessary counterexamples to show that all these properties define pairwise different classes of logics. Consequently, we obtain a new hierarchy of logics going beyond the scope of finitarity.
2017
Lavicka, T., Noguera, C. (2017). A New Hierarchy of Infinitary Logics in Abstract Algebraic Logic. STUDIA LOGICA, 105(3), 521-551 [10.1007/s11225-016-9699-3].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/1200680