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This question is sparked by the current series of The Tudors on BBC television.
A son is born to Queen Katherine in 1541, let's call him Edmund. He grows up to be a healthy boy. When Edward VI dies in 1553 will Prince Edmund succeed to the throne? He would be aged 11 or 12.
Also how does giving birth to a son affect the fortunes of Queen Katherine? Henry would not want to have her executed.