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We reconsider the problem of BRST quantization of a mechanics with infinitelyreducible first class constraints. Following an earlier recipe [Phys. Lett. B381, 105, (1996)], the original phase space is extended by purely auxiliaryvariables, the constraint set in the enlarged space being first stage ofreducibility. The BRST charge involving only a finite number of ghost variablesis explicitly constructed.Comment: 5 pages, LaTex. Minor corrections including the title. The version to  appear in Phys. Rev.

Consistent Batalin-Fradkin quantization of infinitely reducible first class constraints