Σ^1_1 Sets

Σ₁₁ sets are a class of definable sets in descriptive set theory, representing the sets that can be described as projections (or "shadows") of more complex, well-understood sets in a higher-dimensional space. Specifically, they are the sets that can be obtained by projecting a co-analytic set (a complement of an analytic set) from a product space onto one of its coordinates. These sets include many naturally occurring mathematically significant sets and are important in understanding the hierarchy of definability and complexity within mathematical logic and set theory.