Develop the theory of Borel polymorphisms

Develop a systematic theory of Borel polymorphisms for relational structures H, where a Borel polymorphism is a Borel homomorphism from the countable power H^ℕ to H.

Background

Polymorphisms—homomorphisms from powers H^n to H—play a central role in the algebraic classification of classical CSPs, distinguishing tractable problems via the existence of non-trivial operations. The authors propose a Borel analogue, considering Borel polymorphisms H^ℕ → H, and suggest non-triviality could be captured by non-continuity.

They observe initial phenomena: no non-trivial Borel polymorphisms exist for K_3 and for the structure encoding linear equations over F_2, while one exists for K_2. This motivates a broader, systematic development of Borel polymorphism theory to understand its relationship to complexity in the Borel CSP setting.