In reply to llanberis36:
Depends a bit on weather. I've been up to 5200m in the Andes in just trainers no issue, but I was definitely glad of my double boots on a summit day above 6k when it was super windy (100 kph) and a 3am start as went from a lower camp.
If you have warm feet, and don't mind the chance of a restriction if weather is bad, then you'd probably be totally fine in single boots. Overboots are a faff in my opinion, but they do help.