Hi Don, in your basement the portland cement mixed with ash would probably work pretty good since there won't be much heavy traffic or trucks driving on it.
To test it out, pick a corner in the basement and put down about 4" of ash, then pour on about 1" of portland cement. The cement is a fine, talcum-like powder so beware of the dust.
Mix the two layers together DRY. I think just a rake will do, maybe need a hoe or shovel to flip the mix a bit.
The wet it down with a hose or sprinkler can. and smooth out. If your basement is naturally wet/damp it may get enough moisture from the ground to set.
Test it a few days later, to see if it is what you want on the whole floor.
I have a dirt floor in my basement too, but it is dry, and I have some pretty bad areas in some farm roads out back, so my several cubic yards of ash will be road-topping soon.