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Solvability of Rado systems in D-sets
Authors:M. Beiglb  ck, V. Bergelson, T. Downarowicz,A. Fish
Affiliation:aFaculty of Mathematics, University of Vienna, Nordbergstrasse 15, A-1090 Wien, Austria;bThe Ohio State University, Department of Mathematics, 100 Math Tower, 231 West 18th Avenue, Columbus, OH, United States;cInstitute of Mathematics and Computer Science, Wroclaw University of Technology, Poland
Abstract:Rado's Theorem characterizes the systems of homogeneous linear equations having the property that for any finite partition of the positive integers one cell contains a solution to these equations. Furstenberg and Weiss proved that solutions to those systems can in fact be found in every central set. (Since one cell of any finite partition is central, this generalizes Rado's Theorem.) We show that the same holds true for the larger class of D-sets. Moreover we will see that the conclusion of Furstenberg's Central Sets Theorem is true for all sets in this class.
Keywords:Central sets   D-sets   Rado system
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