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-ˇCech compactification of the discrete space of natural numbers. We also obtain connections with nonstandard models of arithmetic.
Finite Embeddability of Sets and Ultrafilters
DI NASSO, MAURO;
2015-01-01
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-ˇCech compactification of the discrete space of natural numbers. We also obtain connections with nonstandard models of arithmetic.File in questo prodotto:
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