A method I have used for interior posts in that very scenario is to fabricate 8"x8" "frames" from 2"x2" steel tubing. This leaves a 4x4" opening that a 4x4" stub tenon on the bottom of your post will sit in to prevent lateral movement. The steel frames are secured to the concrete using one of several methods available. Baseboard trim hides the steel afterwards.
And, like Mike said, to hold the posts down, I weld steel strapping to the outside face of perimeter post bases and posts with at least one hidden face. Wall framing hides these straps.
(I have pictures but never caught on on on how to post)
Take care with the slab though. Point loads at post locations, especially the perimeter and corners, put your slab in danger of cracking. Are you in frost country?