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A Characterization of the Classes of Finite Tree Frames Which are Adequate for the Intuitionistic Logic
Author(s) -
Kirk Robert E.
Publication year - 1980
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.19800263202
Subject(s) - citation , characterization (materials science) , computer science , tree (set theory) , mathematics , discrete mathematics , combinatorics , information retrieval , library science , materials science , nanotechnology
This article provides necessary and sufficient conditions for a class of Kripke frames consisting of finite trees, to be characteristic for the intuitionistic propositional logic I . In particular, Theorem 1 gives an algebraic proof of the adequacy of the Jaskowski and related classes of frames for I . Prel iminaries . By a Kripke frame we understand a triple '$1 = ( A , 2 , O ) where A is a non-empty set and 2 is a partial ordering of A in which 0 is the unique minimal element. An assignment in a Kripke frame a is a function assigning to each propositional formula q and a E A an element of (0, 1}, denoted [q],, satisfying the conditions: