That depends on how the roof and walls were constructed.

Best guess is you will need to rebuild the entire roof to allow the cathedral ceiling to be done.

So, very difficult and expensive.

And messy.

If you remove the ceiling and leave the ceiling joists in place so they continue to act as "rafter ties" the structure would not need to be altered but it might be difficult to make the ties look good.

In order to remove the joist/ties you would need to install a beam at the ridge for the full width of the space and provide support posts at the ends down to the foundation. If the rafters already meet the building code for their span, they would not need to be changed and the loading on the exterior walls would be reduced by half.

In any case, you would need to add insulation between the rafters and add drywall.

Working above your head is always difficult.

"Working above your head is always difficult.''

Ba-boom-pah! LOL!

In most cases this would be difficult structurally, and quite expensive. You can't just remove the ceiling since the joists that the ceiling sheetrock is nailed to typically support the walls, and keep them from being pushed outward by the weight of the roof. My house was designed for the kind of ceiling you describe, and it needs steel tie rods from one side of the living room to the other -- every 4' -- to offset the downward force of the roof.

Steel tie rods would work but would probably require an engineer to design since that solution is unlikely to be shown in the local building code Placing them 4 ft o.c. might require horizontal reinforcing along the top of each wall unless they have double 2x6 top plates. I've been able to put rafter ties 10ft apart with a horizontal LVL beam along the top of a wall.

I just got a drawing from an engineer that can't be built cost effectively as specified. Beware.