Extension Properties and Subdirect Representation in Abstract Algebraic Logic

This paper continues the investigation, started in Lávi?ka and Noguera (Stud Log 105(3): 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, (completely) 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 over arbitrary algebras of the logic. We show that in general the answer is negative, obtaining a richer hierarchy of pairwise different classes of infinitary logics that we separate with natural examples. As by-products we obtain a characterization of subdirect representation for arbitrary logics, develop a fruitful new notion of natural expansion, and contribute to the understanding of semilinear logics.     

“SERVING GOD,FATHERLAND, AND LANGUAGE”: ALCOVER,CATALAN, AND SCIENCE

This article intends to contribute to the science–religion historiography with two topics—philology and the construction of national identities—that can help provide a more complex picture of the relations between science and religion. We use the life and work of the Mallorcan Catholic priest Antoni Maria Alcover (1862–1932) as a case study that puts language, linguistics, and nationalism on the board of science and religion studies. Alcover was the main driving force of the Catalan Dictionary, a collective enterprise that set out to inventory the complete oral and literary lexicon of this language, and which mobilized thousands of people, many of which were clergymen, from all over the Catalan‐speaking territories. In the article, we will explore Alcover's education; the way he established a link between language, religion, and fatherland; the shaping of his identity as a philologist in the image mainly of new German notions and practices; as well as his role in the institutionalization process of the Catalan language as a scientific language, as a language for science and for religion.