The Separation property, the Reduction property and the Uniformization property, introduced in the 1920's and 1930's are three classical regularity properties of pointclasses of the reals.

The celebrated results of Y. Moschovakis on the one hand and D. Martin, J. Steel and H. Woodin on the other, yield a global description of the behaviour of these regularity properties for projective pointclasses under the assumption of large cardinals. These results, impressive as they are, still leave open a lot of natural questions. To name a few we mention:

Do we need large cardinals to obtain their effects on the behaviour of these regularity property?

Is the \(\Sigma^1_{2n+1}\)-separation property actually consistent for \(n > 1\)? More generally: to what extent can we produce set theoretic universes which display a different behaviour of these regularity properties?

Are the separation the reduction and the uniformization property different notions at all?

The goal of this talk to introduce the three mentioned regularity properties, present a couple of these natural problems and discuss new results, utilising a novel forcing technique, which answer some of them.