Weak arithmetics and Kripke models (Q2776821)
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scientific article; zbMATH DE number 1716777
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Weak arithmetics and Kripke models |
scientific article; zbMATH DE number 1716777 |
Statements
14 July 2002
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Heyting arithmetic
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Kripke models
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intuitionistic least number principle
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intuitionistic induction scheme
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forcing
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satisfaction
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Weak arithmetics and Kripke models (English)
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The paper contains two main results. The first shows that the intuitionistic least number principle for \(\Pi_1\) formulas is equivalent to the intuitionistic induction scheme for \(\Pi_1\) formulas. The other result is a characterization of those linear Kripke structures which decide all \(\Delta_0\)-formulas, and in which forcing and satisfaction for \(\Pi_n\) formulas coincide. As a corollary, it is shown that a linear Kripke model which satisfies the Principle of Excluded Middle for formulas in prenex normal form, satisfies the Principle of Excluded Middle for all formulas.
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