2014/01/30 by Dan Hathaway, Hathaway, Dan
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis #math.LO
paper · pdf · doi:10.48550/arxiv.1401.7948
9 pages
openalex publication_date 2014/01/30 · arxiv created 2014/05/04 · arxiv updated 2014/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show a new proof for the fact that when κ and λ are infinite cardinals satisfying λ^ κ= λ, the cofinality of the set of all functions from λ to κ ordered by everywhere domination is 2λ. An earlier proof was a consequence of a result about independent families of functions. The new proof follows directly from the main theorem we present: for every A ⊆ λ there is a function f: κλ → κ such that whenever M is a transitive model of \textrmZF such that κλ ⊆ M and some g: κλ → κ in M dominates f, then A ∈ M. That is, "constructibility can be reduced to domination".