1. A method of garbage collection comprising: A) providing a computer system that includes memory and executes a mutator that modifies references in a dynamically allocated heap in the memory; B) configuring the computer system to act as a garbage collector that: i) scans at least some of the heap for references; ii) treats at least a portion of the heap as divided into heap sections with each of at least some of which the garbage collector associates a respective remembered set of reference-location identifiers, recorded in respective slots in a remembered-set table associated with that remembered set and thereby with that heap section, that identify regions where references to objects in that heap section have been found; iii) executes in a plurality of garbage-collector threads a remembered-set-maintenance operation in which: a) at least one of the garbage-collector threads performs a table-replacement operation, which, for a given remembered-set table, includes: (1) an old-table-transfer operation, in which reference-location identifiers that identify regions containing all locations contained in regions identified by the reference-location identifiers in the remembered-set table, denominated the old remembered-set table, that is associated with a given remembered set are placed into a new remembered-set table; and (2) a table-installation operation, in which the old remembered-set table is replaced with the new remembered-set table; b) at least another one of the garbage-collector threads performs a reference-recording operation, which, for a given reference to an object in a given heap section, includes: (1) in at least some instances in which the given heap section is currently being replaced by a different garbage-collector thread, performing at least one table-access operation, in which a target slot chosen in accordance with a placement rule is accessed; (2) at least if that remembered-set table is not currently undergoing replacement, making a table-update attempt, in which an attempt is made to place a table-location identifier into the target slot if necessary to ensure that the given reference's location is included in a region identified by a reference-location identifier in that remembered-set table; (3) in at least some instances, making a replacement-status determination, in which a determination is made of whether that table is currently undergoing replacement; (4) in at least some instances in which the replacement-status determination is affirmative, performing a record-addition operation, which includes placing an insertion record containing such a reference-location identifier into an insertion-record list associated with the given heap section; and (5) refraining from performing a record-addition operation if the replacement-status determination is negative; and c) if an insertion-record list is associated with the given remembered set, the table-replacement operation includes performing a record-transfer operation, in which, for each reference-location identifier contained in an insertion record in such an insertion-record list, a table-location identifier is placed in the new table if necessary to ensure that the regions identified by the reference-location identifiers in the new table include the region identified by the reference-location identifier contained in that insertion record; iv) employs the remembered sets thereby maintained to identify potentially reachable objects; v) reclaims memory space occupied by objects not identified as potentially reachable; and C) employing the computer system to execute the garbage collector.