0469118 20240103213358.220170116235959.9 85007165633 000401436800004 10.1007/s11225-016-9699-3 31 s. P cav_un_epca*02921900039-32151053 (2017)521-551Springer Abstract algebraic logic consequence relations infinitary logics completeness properties cav_un_auth*0332685 Lávička Tomáš Oddělení teoretické informatiky Department of Theoretical Computer Science UIVT-O Department of Theoretical Computer Science Ústav informatiky AV ČR, v. v. i. cav_un_auth*0293476 Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory Noguera Carles UTIA-B K Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2017/MTR/noguera-0469118.pdf cav_un_auth*0292719 GA13-14654S GA ČR cav_un_auth*0339025 689176 EC XE 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. BA 10000 10100 10101 2018 UIVT-O 10000 10200 10201 4 A 4a 20231122142202.9 UIVT-O BA RVO:67985556 RVO:67985807 http://hdl.handle.net/11104/0269760 S n.a. Article Mathematics|Logic|Philosophy LOGIC|MATHEMATICS 0.600 0.13 12 0.00118 0.331 753 0.353 0.320 46 Q3 21.596 21.9 Q4 Q3 1.15 Q1 27.5 2017 Soubory v repozitáři: a0469118.pdf 85007165633 SCOPUS PUBMED 000401436800004 WOS cav_un_epca*0292190 Studia Logica 0039-3215 1572-8730 Roč. 105 č. 3 2017 521 551 Springer