We have 110 year old pine floor in our kitchen which is breaking up in places

1st option: lift boards where damage exists, cut back to the nearest joist making the cut over the middle of the joist and install new board, once the floor is repaired screw 12mm ply over it at every 200mm use screws with a length that will not penetrate through the floor boards so's not to hit any wires or pipes. then you may need to alter doors/architraves or skirting to accommodate the new finished floor level (ffl) 2nd option (prefered): take it up, clean the top of the exposed joists checking for nails etc, also take the time to check the condition of the joists to make sure the are sound especially at the bearing points, repair or replace where necessary, then lay a minimum of 18mm Ply perpendicular to the Joists fixing every 200mm leave a 2-3mm gap between boards for expansion and support all abutments with timber underneath (3 x 2 will suffice)