A Syntactic and Categorical Derivation of G "odel's Completeness\n Theorem

2021/11/10 by Hugo Jenkins, Jenkins, Hugo
Computer Science · Mathematics · Medicine · #03G30 (Primary) 03F03 #18C10 (Secondary) #Advanced Algebra and Logic #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2111.05998

openalex publication_date 2021/11/10 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

Considering classical first-order logic with equality, we give a "fully\nsyntactic" construction of the (weak) syntactic category \Syn(T)\nassociated to a consistent theory T; we show it is a consistent coherent\ncategory; and we show that a morphism of coherent categories \Syn(T)\→\n bfSet gives rise to a model \M of T in the usual sense. We\nthen invoke Deligne's theorem on small consistent coherent categories.\n

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