2019/06/29 by Trevor M. Wilson, Wilson, Trevor M.
Computer Science · Mathematics · #03E55 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.1907.00284
openalex publication_date 2019/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that Weak Vop venka's Principle, which is the statement that the\nopposite category of ordinals cannot be fully embedded into the category of\ngraphs, is equivalent to the large cardinal principle Ord is Woodin, which says\nthat for every class C there is a C-strong cardinal. Weak Vop venka's\nPrinciple was already known to imply the existence of a proper class of\nmeasurable cardinals. We improve this lower bound to the optimal one by\ndefining structures whose nontrivial homomorphisms can be used as extenders,\nthereby producing elementary embeddings witnessing C-strongness of some\ncardinal.\n