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Completeness of intermediate logics with doubly negated axioms
Author(s) -
Ardeshir Mohammad,
Mojtahedi S. Mojtaba
Publication year - 2014
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.201200083
Subject(s) - negation , axiom , mathematics , intuitionistic logic , closure (psychology) , completeness (order theory) , intermediate logic , class (philosophy) , kripke semantics , discrete mathematics , description logic , propositional calculus , linguistics , computer science , theoretical computer science , artificial intelligence , philosophy , mathematical analysis , geometry , economics , market economy
Let L denote a first‐order logic in a language that contains infinitely many constant symbols and also containing intuitionistic logic IQC . By ¬ ¬ L , we mean the associated logic axiomatized by the double negation of the universal closure of the axioms of L plus IQC . We shall show that if L is strongly complete for a class of Kripke models K , then ¬ ¬ L is strongly complete for the class of Kripke models that are ultimately in K .