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An extension of ono's completeness result
Author(s) -
Suzuki NobuYuki
Publication year - 1990
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19900360410
Subject(s) - completeness (order theory) , citation , extension (predicate logic) , computer science , library science , mathematics , programming language , mathematical analysis
The ore m 1. Let {M, , Mz , . . . , M,, . . . , Mu} be the enumeration of propositional logics in the second slice Y2 (see HOSOI-ONO [l]), and D be the sentence V x ( p ( x ) v q ) =I ( V x p ( x ) v q ) . For each J E Y2, we denote by J* + D the intermediate predicate logic obtained from the minimum predicate extension J* of J by adding D as a new axiom. Then, for each n (1 5 n < w ) , M,* + D is complete with respect to the class of Kripke structures having constant domain, with height at most 2 and having at most n maximal elements. Moreover, M,* + D is complete with respect to the class of Kripke structures having constant domain and with height at most 2.