Infinitary first-order categorical logic |
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Authors: | Christian Espíndola |
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Institution: | Department of Mathematics, Masaryk University, Kotlá?ská 2 (611 37) Brno, Czech Republic |
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Abstract: | We present a unified categorical treatment of completeness theorems for several classical and intuitionistic infinitary logics with a proposed axiomatization. This provides new completeness theorems and subsumes previous ones by Gödel, Kripke, Beth, Karp and Joyal. As an application we prove, using large cardinals assumptions, the disjunction and existence properties for infinitary intuitionistic first-order logics. |
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Keywords: | 03G30 03C75 18B25 18C50 Categorical logic Infinitary logics Completeness theorems Sheaf models Large cardinals |
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