Infinitary first-order categorical logic
Logic
2019-01-01 v1 Category Theory
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.
Keywords
Cite
@article{arxiv.1701.01301,
title = {Infinitary first-order categorical logic},
author = {Christian Espíndola},
journal= {arXiv preprint arXiv:1701.01301},
year = {2019}
}