Descriptive Set Theory Over Hyperfinite Sets

H. Jerome Keisler, Kenneth Kunen, Arnold Miller, Steven Leth
Journal of Symbolic Logic, Vol. 54, No. 4. (Dec., 1989), pp. 1167-1180.


The separation, uniformization, and other properties of the Borel and projective hierarchies over hyperfinite sets are investigated and compared to the corresponding properties in classical descriptive set theory. The techniques used in this investigation also provide some results about countably determined sets and functions, as well as an improvement of an earlier theorem of Kunen and Miller.