Title: Generalizing Erdős B-free systems: Erdős Sieves
Abstract: Given a set B = {b_1,b_2,...} of pairwise coprime numbers, we say it forms a B free system, if sum_i 1/b_i is finite. If for each i we instead consider a set of congruence classes mod b_i, we get Erdős sieves. For a sieve R we investigate the dynamical systems associated to the R-free numbers, those integers not contained in any congruence class of the sieve. We show how admissible sets of B-free systems can be seen as R-free numbers of different sieves, and how this elucidates many arguments from the theory of B-free systems. We will also give examples of interesting sets which can be realized as the R-free numbers of some sieve R.