Complexity Reduction in Combinatorial Set Theory
Yipu Li

Abstract:
In this thesis, we study complexity reduction problems that originate from the analysis of definable combinatorial objects. We make significant progress in lifting a family of complexity reduction results to higher point classes. Specifically, we isolate a property we call Functional Projection that makes the complexity reduction proofs lift, and we establish that Functional Projection holds for all projective levels in the model L and L[U]. As a consequence, we derive the existence of combinatorial objects in L[U] at the optimal projective level \Pi^1_2.