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FilledSmallSquareEvaluator is an option for Cell which gives the name of the kernel to use to evaluate the contents of a cell.

FilledSmallSquare The default setting is typically Evaluator->"Local".

FilledSmallSquareEvaluator is more often set at a global level or at the level of whole notebooks than at the level of individual cells.

FilledSmallSquare See The Mathematica Book: Section 2.10.2 and Section 2.10.9.

FilledSmallSquare See also: InitializationCell.