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Löb operators and interior operators

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Löb operators and interior operators RENDICONTI del SEMINARIO MATEMATICO della UNIVERSITÀ DI PADOVA GIULIANOMAZZANTI MASSIMOMIROLLI Löb operators and interior operators Rendiconti del Seminario Matematico della Università di Padova, tome 65 (1981), p. 77-84. <> © Rendiconti del Seminario Matematico della Università di Padova, 1981, tous droits réservés. L’accès aux archives de la revue « Rendiconti del Seminario Matematico della Università di Padova » ( implique l’ac- cord avec les conditions générales d’utilisation ( php). Toute utilisation commerciale ou impression systématique est consti- tutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques Löb Operators and Interior Operators. GIULIANO MAZZANTI - MASSIMO MIROLLI (*) SUMMARY - In the theory of Boolean algebras, many kinds of operators have been studied: for istance the ones called Lob operators (see [3] and [5]) and interior operators (see [3] and [4]). In this paper we analyze some links between these two types of operators and in particular we give a characterization of the interior operator which may be expressed by x · zx where T is a L6b operator. It can be noticed that, using the language of modal logic, this interior operator is nothing else but Smorynski’s modal operator s (see [6]). SUNTO - Sono state ampiamente studiate le algebre di Boole con un operatore di L6b (vedi [3] e [5]) e quelle con un operatore di interno (vedi [3] e [4]). In questo lavoro si analizzano alcuni legami tra questi operatori. In parti- colare si caratterizzano gli operatori di interno esprimibili mediante x. TX (T 6 un operatore di da rilevare che, tradotto nel linguaggio della logica modale, a questo operatore di interno corrisponde l’ope

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