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A new hierarchy of infinitary logics in abstract algebraic logic
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SYSNO ASEP 0469118 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title A new hierarchy of infinitary logics in abstract algebraic logic Author(s) Lávička, Tomáš (UIVT-O)
Noguera, Carles (UTIA-B) RID, ORCIDSource Title Studia Logica. - : Springer - ISSN 0039-3215
Roč. 105, č. 3 (2017), s. 521-551Number of pages 31 s. Publication form Print - P Language eng - English Country NL - Netherlands Keywords Abstract algebraic logic ; consequence relations ; infinitary logics ; completeness properties Subject RIV BA - General Mathematics OECD category Pure mathematics Subject RIV - cooperation Institute of Computer Science - General Mathematics R&D Projects GA13-14654S GA ČR - Czech Science Foundation (CSF) Institutional support UTIA-B - RVO:67985556 ; UIVT-O - RVO:67985807 UT WOS 000401436800004 EID SCOPUS 85007165633 DOI https://doi.org/10.1007/s11225-016-9699-3 Annotation 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. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2018
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