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A forcing order has the countable chain condition when every antichain in a forcing order is countable. Such forcing preserves cardinals and cofinalities at least ${\aleph }_1$.

For a forcing order with the countable chain condition for forcing, a real can be represented by a nice name determined by a countable antichain in a forcing order for each natural-number coordinate. This bounds the number of reals in the extension in terms of the size of the forcing order.