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arXiv · 1701.01301

Infinitary first-order categorical logic

Christian Espíndola
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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 G\"odel, Kripke, Beth, Karp, Joyal, Makkai and Fourman/Grayson. As an application we prove, using large cardinals assumptions, the disjunction and existence properties for infinitary intuitionistic first-order logics.

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Christian Espíndola. 2017-01-05. Infinitary first-order categorical logic. https://arxiv.org/abs/1701.01301

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