A non-hyperarithmetical Gödel logic (Q2151390)
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| Language | Label | Description | Also known as |
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| English | A non-hyperarithmetical Gödel logic |
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A non-hyperarithmetical Gödel logic (English)
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1 July 2022
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The logic investigated in this paper is first-order Gödel logic with truth values given by the set \(\{0\} \cup \{1/n \mid n \in N\setminus \{0\}\}\). It is shown that the set of valid formulas in such logic is \(\Pi_1^1\) complete and that the set of satisfiable formulas is \(\Sigma_1^1\) complete, strengthening previous results. The main tools used in the paper are properties of Kripke-Platek set theory and results involving admissible sets. For the entire collection see [Zbl 1490.03004].
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first-order Gödel logic
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complexity
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