On Rado's theorem and its related problems

نویسندگان

1 Department of Mathematics, University of Guilan, Rasht, Guilan, Iran

2 Department of Mathematics, University of Guilan, Rasht, Guilan, Iran

doi
10.22091/maa.2023.9445.1002
چکیده

In this paper, we state Rado's theorem, Ramsey families, and their connections with ergodic theory and combinatorial problems. We discuss the historical development of these concepts since their inception to how some problems in the fields of combinatorics and number theory were formulated and solved, particularly through the lens of dynamical systems. We also address some open questions in this field.