caa a22 4500 469126906 CHVBK 20180323133153.0 cr unu---uuuuu 170328e19920101xx s 000 0 eng 10.1007/BF01270395 doi (NATIONALLICENCE)springer-10.1007/BF01270395 The logic of II 1-conservativity continued [Elektronische Daten] [Petr Hájek, Franco Montagna] It is shown that the propositional modal logic IRM (interpretability logic with Montagna's principle and with witness comparisons in the style of Guaspari's and Solovay's logicR) is sound and complete as the logic ofII 1-conservativity over each∑ 1-sound axiomatized theory containingI∑ 1. The exact statement of the result uses the notion of standard proof predicate. This paper is an immediate continuation of our paper [HM]. Knowledge of [HM] is presupposed. We define a modal logic, called IRM, which includes both ILM andR (the logic of [GS]) and prove an arithmetical completeness theorem in the style of [GS], thus showing that IRM is the logic ofII 1-conservativity with witness comparisons. The reader is recommended to have Smoryński's book [Sm] at his/her disposal. Springer-Verlag, 1992 Hájek Petr Institute of Computer and Information Science, ČSAV, Pod vodárenskou věži 2, CS-18207, Praha, Czechoslovakia aut Montagna Franco Scuola di Spezializzazion e in Logica Matematica, Universitá di Siena, I-5300, Siena, Italy aut Archive for Mathematical Logic Springer-Verlag 32/1(1992-01-01), 57-63 0933-5846 32:1<57 1992 32 153 https://doi.org/10.1007/BF01270395 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01270395 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hájek Petr Institute of Computer and Information Science, ČSAV, Pod vodárenskou věži 2, CS-18207, Praha, Czechoslovakia aut NATIONALLICENCE 700 1- Montagna Franco Scuola di Spezializzazion e in Logica Matematica, Universitá di Siena, I-5300, Siena, Italy aut NATIONALLICENCE 773 0- Archive for Mathematical Logic Springer-Verlag 32/1(1992-01-01), 57-63 0933-5846 32:1<57 1992 32 153 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer