On the compactness property of extensions of first-order Gödel logic

We study three kinds of compactness in some variants of G\"odel logic: compactness, entailment compactness, and approximate entailment compactness. For countable first-order underlying language we use the Henkin construction to prove the compactness property of extensions of first-order G\"...

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Published in:arXiv.org 2014-10
Main Author: Seyed Mohammad Amin Khatami
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description We study three kinds of compactness in some variants of G\"odel logic: compactness, entailment compactness, and approximate entailment compactness. For countable first-order underlying language we use the Henkin construction to prove the compactness property of extensions of first-order G\"odel logic enriched by nullary connective or the Baaz's projection connective. In the case of uncountable first-order language we use the ultraproduct method to derive the compactness theorem
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title On the compactness property of extensions of first-order Gödel logic
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