Borel version of the Local Lemma
  We prove a Borel version of the local lemma, i.e. we show that, under suitable assumptions, if the set of variables in the local lemma has a structure of a Borel space, then there exists a satisfying assignment which is a Borel function. The main tool which we develop for the proof, which is of independent interest, is a parallel version of the Moser-Tardos algorithm which uses the same random bits to resample clauses that are far enough in the dependency graph. 
Endre Cs\'oka, {\L}ukasz Grabowski, Andr\'as M\'ath\'e, Oleg Pikhurko,   Konstantinos Tyros
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