Abstract:
The authors propose a general effective method for constructing a predicate calculus complete with respect to $L_n$-general validity in quasi-Hilbert form (i.e. in Hilbert form but using a language extended by finitely many “external metasymbols”) on the basis of an arbitrary many-valued logic. For logics in a fairly large class containing many of the logics studied previously, a general effective method is indicated for constructing a predicate calculus of Hilbert type complete with respect to $L_n$-general validity. The results and methods of the article make it possible to initiate the development of model theory on the basis of an arbitrary finite-valued logic.
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