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Title: Kripke model theory
 
Abstract: Let L be a first-order language. An L-Kripke
structure  can be considered as a class of classical
L-structures partially ordered by the relation weak
substructure.The forcing relation for K is defined in the usual
way. The relations substructure and elementary substructure
between Kripke structures can be defined in several ways. We
choose ones that we think are the right ones and develop basic
Kripke model theory based on them. Most notably, we prove
suitable versions of Tarski's test, upward and downward L-S
theorems and some preservation theorems.
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