2014/05/12 by Andreas Blass, Blass, Andreas, Mauro Di Nasso +1
Computer Science · Mathematics · #03E05 (Primary) #03H15 #11U10 (Secondary) #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis #math.LO #msc:03E05 #msc:03H15 #msc:11U10
paper · pdf · doi:10.48550/arxiv.1405.2841
to appear in Bulletin of the Polish Academy of Sciences, Math Series
openalex publication_date 2014/05/12 · arxiv created 2015/12/10 · arxiv updated 2015/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A set A of natural numbers is finitely embeddable in another such set B if every finite subset of A has a rightward translate that is a subset of B. This notion of finite embeddability arose in combinatorial number theory, but in this paper we study it in its own right. We also study a related notion of finite embeddability of ultrafilters on the natural numbers. Among other results, we obtain connections between finite embeddability and the algebraic and topological structure of the Stone-Cech compactification of the discrete space of natural numbers. We also obtain connections with nonstandard models of arithmetic.