I spent an hour this morning trying to get the remainder of the post out of its concrete housing, but to no avail. It must be about a foot deep and I managed to get down maybe three inches:
The problem is that the wood is all soggy and flexible, so I can't get any purchase on it. I screwed a six-inch screw into it and when I pulled on it it just slid out. I tried to drill it out, but all the wood fibres are running upwards and they just move when drilled, they don't come out. Worse, horrible ooze the colour of Caramac rises up out of the holes if I drill too deeply (as in, more than about six inches). I managed to get down as far as I did by using a cold chisel to separate the wood from the concrete then hammering it into the side of the wood to lever it out. This isn't going to work for much longer, though, because I won't be able to get the angle.
I can see three kinds of tool that might get it out:
1) A monster corkscrew, with maybe a two-inch diameter.
2) One of those circular tools people use for making boreholes in soil.
3) Something like a screwdriver but with movable flanges on the side that will go down smoothly then bite into the wood when pulled back out.
Dynamite would also perhaps work.