Finite Embeddability of Sets and Ultrafilters

Andreas Blass, and Mauro Di Nasso. "Finite Embeddability of Sets and Ultrafilters." Bulletin of the Polish Academy of Sciences. Mathematics 63.3 (2015): 195-206. <http://eudml.org/doc/281202>.

@article{AndreasBlass2015,
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-Čech compactification of the discrete space of natural numbers. We also obtain connections with nonstandard models of arithmetic.},
author = {Andreas Blass, Mauro Di Nasso},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {ultrafilter; nonstandard models; shift map},
language = {eng},
number = {3},
pages = {195-206},
title = {Finite Embeddability of Sets and Ultrafilters},
url = {http://eudml.org/doc/281202},
volume = {63},
year = {2015},
}

TY - JOUR
AU - Andreas Blass
AU - Mauro Di Nasso
TI - Finite Embeddability of Sets and Ultrafilters
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2015
VL - 63
IS - 3
SP - 195
EP - 206
AB - 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.
LA - eng
KW - ultrafilter; nonstandard models; shift map
UR - http://eudml.org/doc/281202
ER -