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-Čech compactification of the discrete space of natural numbers. We also obtain connections with nonstandard models of arithmetic.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba8024-1-2016,
author = {Andreas Blass and Mauro Di Nasso},
title = {Finite Embeddability of Sets and Ultrafilters},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {63},
year = {2015},
pages = {195-206},
zbl = {06545366},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba8024-1-2016}
}
Andreas Blass; Mauro Di Nasso. Finite Embeddability of Sets and Ultrafilters. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 63 (2015) pp. 195-206. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba8024-1-2016/