Finite Embeddability of Sets and Ultrafilters

Andreas Blass; Mauro Di Nasso

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arXiv · 1405.2841

Finite Embeddability of Sets and Ultrafilters

Andreas Blass·Mauro Di Nasso

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Abstract

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.

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BibTeX RIS

Andreas Blass, Mauro Di Nasso. 2014-05-12. Finite Embeddability of Sets and Ultrafilters. https://arxiv.org/abs/1405.2841

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