arXiv:1405.2841 Abstract | arXiv Analytics

arXiv:1405.2841 [math.LO]Abstract References Reviews Resources

Finite Embeddability of Sets and Ultrafilters

Published 2014-05-12, updated 2015-12-10Version 3

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.

Comments: to appear in Bulletin of the Polish Academy of Sciences, Math Series

Categories: math.LO

Subjects: 03E05, 03H15, 11U10

Keywords: natural numbers, ultrafilters, finite embeddability arose, combinatorial number theory, finite subset

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