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We show that if there is no family of cardinality less than c which dominates uoi, then the box product of countably many compact first-countable spaces is paracompact; hence the countable box product of compact metrizable spaces is paracompact if 2" = o>2. We also give classes of forcing extensions in which many box products are paracompact.doi:10.2307/2042125 fatcat:brhs2i7njbgxfa7vnck7vuht5q