A new hierarchy of infinitary logics in abstract algebraic logic

0469118 - ÚTIA 2018 RIV NL eng J - Journal Article
Lávička, Tomáš - Noguera, Carles
A new hierarchy of infinitary logics in abstract algebraic logic.
Studia Logica. Roč. 105, č. 3 (2017), s. 521-551. ISSN 0039-3215. E-ISSN 1572-8730
R&D Projects: GA ČR GA13-14654S
EU Projects: European Commission(XE) 689176 - SYSMICS
Institutional support: RVO:67985556 ; RVO:67985807
Keywords : Abstract algebraic logic * consequence relations * infinitary logics * completeness properties
OECD category: Pure mathematics; Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) (UIVT-O)
Impact factor: 0.450, year: 2017
http://library.utia.cas.cz/separaty/2017/MTR/noguera-0469118.pdf

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.
Permanent Link: http://hdl.handle.net/11104/0269760