caa a22 4500 465743781 CHVBK 20180323111814.0 cr unu---uuuuu 170327e19900301xx s 000 0 eng 10.1007/BF01634981 doi (NATIONALLICENCE)springer-10.1007/BF01634981 The logic of π1-conservativity [Elektronische Daten] [Petr Hájek, Franco Montagna] We show that the modal prepositional logicILM (interpretability logic with Montagna's principle), which has been shown sound and complete as the interpretability logic of Peano arithmetic PA (by Berarducci and Savrukov), is sound and complete as the logic ofπ 1-conservativity over eachbE 1-sound axiomatized theory containingI⌆ 1 (PA with induction restricted tobE 1-formulas). Furthermore, we extend this result to a systemILMR obtained fromILM by adding witness comparisons in the style of Guaspari's and Solovay's logicR (this will be done in a separate continuation of the present paper). Springer-Verlag, 1990 Hájek Petr Mathematical Institute CSAV, Zitna 25, CS-11567, Praha, Czechoslovakia aut Montagna Franco Scuola di Specializzazione in Logica Matematica, Universitá di Siena, I-53100, Siena, Italy aut Archive for Mathematical Logic Springer-Verlag 30/2(1990-03-01), 113-123 0933-5846 30:2<113 1990 30 153 https://doi.org/10.1007/BF01634981 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01634981 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hájek Petr Mathematical Institute CSAV, Zitna 25, CS-11567, Praha, Czechoslovakia aut NATIONALLICENCE 700 1- Montagna Franco Scuola di Specializzazione in Logica Matematica, Universitá di Siena, I-53100, Siena, Italy aut NATIONALLICENCE 773 0- Archive for Mathematical Logic Springer-Verlag 30/2(1990-03-01), 113-123 0933-5846 30:2<113 1990 30 153 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer