1Maxwell Institute of Mathematical Sciences and the School of Mathematics, University of Edinburgh, JCMB, The King’s Buildings, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, Scotland
we discuss a framework for constructing large subsets of and for non-archimedean local fields . This framework is applied to obtain new estimates for the Hausdorff dimension of angle-avoiding sets and to provide a counterexample to a limiting version of the Capset problem.
