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  1. Filter pairs and natural extensions of logics.Peter Arndt, Hugo Luiz Mariano & Darllan Conceição Pinto - 2022 - Archive for Mathematical Logic 62 (1):113-145.
    We adjust the notion of finitary filter pair, which was coined for creating and analyzing finitary logics, in such a way that we can treat logics of cardinality $$\kappa $$, where $$\kappa $$ is a regular cardinal. The corresponding new notion is called $$\kappa $$ -filter pair. A filter pair can be seen as a presentation of a logic, and we ask what different $$\kappa $$ -filter pairs give rise to a fixed logic of cardinality $$\kappa $$. To make the (...)
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  • Extension Properties and Subdirect Representation in Abstract Algebraic Logic.Tomáš Lávička & Carles Noguera - 2018 - Studia Logica 106 (6):1065-1095.
    This paper continues the investigation, started in Lávička and Noguera : 521–551, 2017), of infinitary propositional logics from the perspective of their algebraic completeness and filter extension properties in abstract algebraic logic. If follows from the Lindenbaum Lemma used in standard proofs of algebraic completeness that, in every finitary logic, intersection-prime theories form a basis of the closure system of all theories. In this article we consider the open problem of whether these properties can be transferred to lattices of filters (...)
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