A strictly finitary non-triviality proof for a paraconsistent system of set theory deductively equivalent to classical ZFC minus foundation (Q1590193)
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scientific article; zbMATH DE number 1545483
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A strictly finitary non-triviality proof for a paraconsistent system of set theory deductively equivalent to classical ZFC minus foundation |
scientific article; zbMATH DE number 1545483 |
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A strictly finitary non-triviality proof for a paraconsistent system of set theory deductively equivalent to classical ZFC minus foundation (English)
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18 December 2001
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The paraconsistent system CPQ-ZFC/F is defined, where CPQ can be regarded as the first-order logic obtained from classical logic by removing modus ponens. Then CPQ-ZFC/F is a paraconsistent version of classical ZFC minus the axiom of foundation. It is shown using strong nonfinitary methods that CPQ-ZFC/F has the same deductive powers as classical ZFC/F. It is then shown using strictly finitary methods that CPQ-ZFC/F is non-trivial.
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paraconsistent logic
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paraconsistent set theory
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