The prime uses phrases like "open sentence"...

[Joe Horn]

(06-01-2014 07:22 AM)Craig Thomas Wrote:  For those who know, when did this come into vogue and why?

Is this a US thing, or does it see wider use?

According to dictionary.com, "open sentence" dates back to around 1935-40. It doesn't say whether it's an Americanism or not. A good article about open sentences can be found here.