Finite Embeddability of Sets and Ultrafilters
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 63 (2015) no. 3, pp. 195-206
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
set natural numbers finitely embeddable another set every finite subset has rightward translate subset notion finite embeddability arose combinatorial number theory paper study its own right study related notion finite embeddability ultrafilters natural numbers among other results obtain connections between finite embeddability algebraic topological structure stone ech compactification discrete space natural numbers obtain connections nonstandard models arithmetic
Affiliations des auteurs :
Andreas Blass 1 ; Mauro Di Nasso 2
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author = {Andreas Blass and Mauro Di Nasso},
title = {Finite {Embeddability} of {Sets} and {Ultrafilters}},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
pages = {195--206},
publisher = {mathdoc},
volume = {63},
number = {3},
year = {2015},
doi = {10.4064/ba8024-1-2016},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ba8024-1-2016/}
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Andreas Blass; Mauro Di Nasso. Finite Embeddability of Sets and Ultrafilters. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 63 (2015) no. 3, pp. 195-206. doi: 10.4064/ba8024-1-2016
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