Herbrand consistency of some arithmetical theories (Q2915894)
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scientific article; zbMATH DE number 6083954
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Herbrand consistency of some arithmetical theories |
scientific article; zbMATH DE number 6083954 |
Statements
Herbrand consistency of some arithmetical theories (English)
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19 September 2012
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cut-free provability
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Herbrand provability
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Herbrand consistency
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bounded arithmetics
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weak arithmetics
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Gödel's second incompleteness theorem
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0.93369627
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0.9186607
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0.9092159
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0.8860952
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0.8761971
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Herbrand consistency of a theory \(T\) means that every finite Herbrand conjunction of \(T\) is satisfiable. The author modifies a construction by \textit{Z. Adamowicz} [Fundam. Math. 171, No. 3, 279--292 (2002; Zbl 0995.03044)] to establish that \(\mathrm{I}\Delta_0+\Omega_1\) does not prove Herbrand consistency of \(\mathrm{I}\Delta_0\).
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