On the Uniform Projection Problem in Descriptive Set Theory.

For every n ≥ 1 , generic models of ZFC will be presented for either of the following two sentences: 1. There exists a linear Σ n + 2 1 set not equal to the projection of any uniform planar Π n + 2 1 set. 2. There exists a linear Δ n + 2 1 set not equal to the projection of any uniform planar Π n + 1 1 set. Ensuing consistency and independence corollaries are discussed. [ABSTRACT FROM AUTHOR]