0484922 20240103215400.720180117235959.9 85037378516 000450596100001 10.1007/s11225-017-9771-7 31 s. P cav_un_epca*02921900039-32151066 (2018)1065-1095Springer Abstract algebraic logic Infinitary logics Natural extensions Natural expansions Semilinear logics Subdirect representation cav_un_auth*0341114 Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory 50 Lávička Tomáš UTIA-B CZ Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0293476 Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory 50 Noguera Carles UTIA-B A Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2018/MTR/lavicka-0484922.pdf cav_un_auth*0349495 GA17-04630S GA ČR This paper continues the investigation, started in Lávička 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. BA 10000 10100 10101 2019 2 RVO:67985556 http://hdl.handle.net/11104/0280148 S 3+4 Article Mathematics|Logic|Philosophy LOGIC|MATHEMATICS 0.610 0.265 14.6 0.0013 0.393 846 0.474 0.391 49 Q3 30.582 21.2 Q3 Q3 1.02 Q1 27.5 2018 85037378516 SCOPUS PUBMED 000450596100001 WOS cav_un_epca*0292190 Studia Logica 0039-3215 1572-8730 Roč. 106 č. 6 2018 1065 1095 Springer