TY - JOUR
T1 - Using Ultrafilters to Prove Ramsey-type Theorems
AU - Fernández-Bretón, David J.
N1 - Publisher Copyright:
© 2021 The Mathematical Association of America.
PY - 2022
Y1 - 2022
N2 - Ultrafilters are a tool, originating in mathematical logic and general topology, that has steadily found more and more uses in multiple areas of mathematics, such as combinatorics, dynamics, and algebra, among others. The purpose of this article is to introduce ultrafilters in a friendly manner and present some applications to the branch of combinatorics known as Ramsey theory, culminating with a new ultrafilter-based proof of van der Waerden’s theorem.
AB - Ultrafilters are a tool, originating in mathematical logic and general topology, that has steadily found more and more uses in multiple areas of mathematics, such as combinatorics, dynamics, and algebra, among others. The purpose of this article is to introduce ultrafilters in a friendly manner and present some applications to the branch of combinatorics known as Ramsey theory, culminating with a new ultrafilter-based proof of van der Waerden’s theorem.
UR - http://www.scopus.com/inward/record.url?scp=85121792482&partnerID=8YFLogxK
U2 - 10.1080/00029890.2022.2004848
DO - 10.1080/00029890.2022.2004848
M3 - Artículo
AN - SCOPUS:85121792482
SN - 0002-9890
VL - 129
SP - 116
EP - 131
JO - American Mathematical Monthly
JF - American Mathematical Monthly
IS - 2
ER -