0491981 20250112195927.820180806235959.9 85049630574 000478664000007 10.1007/978-3-662-57669-4_7 15 s. P cav_un_epca*0491980978-3-662-57668-70302-9743130-144BerlinSpringer2018MossL. S.de QueirozR.MartinezM. Lindenbaum lemma Pair extension lemma Infinitary logic Infinitary deduction rule Strong disjunction Prime theory cav_un_auth*0218529 Bílková Marta UIVT-O Oddělení teoretické informatiky Department of Theoretical Computer Science Department of Theoretical Computer Science Ústav informatiky AV ČR, v. v. i. cav_un_auth*0100737 Cintula Petr UIVT-O Oddělení teoretické informatiky Department of Theoretical Computer Science Department of Theoretical Computer Science K Ústav informatiky AV ČR, v. v. i. cav_un_auth*0341114 Lávička Tomáš UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory CZ Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0349495 GA17-04630S GA ČR cav_un_auth*0348385 GC16-07954J GA ČR CZ cav_un_auth*0348811 JSPS-16-08 AV ČR CZ JP The abstract Lindenbaum lemma is a crucial result in algebraic logic saying that the prime theories form a basis of the closure systems of all theories of an arbitrary given logic. Its usual formulation is however limited to finitary logics, i.e., logics with Hilbert-style axiomatization using finitary rules only. In this contribution, we extend its scope to all logics with a countable axiomatization and a well-behaved disjunction connective. We also relate Lindenbaum lemma to the Pair extension lemma, other well-known result with many applications mainly in the theory of non-classical modal logics. While a restricted form of this lemma (to pairs with finite right-hand side) is, in our context, equivalent to Lindenbaum lemma, we show a perhaps surprising result that in full strength it holds for finitary logics only. Finally we provide examples demonstrating both limitations and applications of our results. cav_un_auth*0362872 WoLLIC 2018. International Workshop on Logic, Language, Information and Computation /25./ 20180724 Bogotá CO 20180727 BA 10000 10200 10201 2019 UTIA-B 10000 10100 10101 4 E R 4e 4r a 20231122143320.7 A 20250112195927.7 UTIA-B BA RVO:67985807 RVO:67985556 http://hdl.handle.net/11104/0285566 S 3+4 Proceedings Paper Computer Science Artificial Intelligence|Computer Science Theory Methods 0.339 Q2 Q2 2018 Soubory v repozitáři: dodatecne_citace_k_0554811.pdf, a0491981prep.pdf, a0491981.pdf 85049630574 SCOPUS PUBMED 000478664000007 WOS cav_un_epca*0491980 Logic, Language, Information and Computation Springer 2018 Berlin 130 144 978-3-662-57668-7 Lecture Notes on Computer Science 10944 0302-9743 340 Moss L. S. 340 de Queiroz R. 340 Martinez M.