We study power-set operations on classes of trees and tree algebras. Our main result consists of a distributive law between the tree monad and the upwards-closed power-set monad, in the case where all trees are assumed to be linear. For non-linear ones, we prove that such a distributive law does not exist.

@article{paperbot2186,
  title = {The Power-Set Construction for Tree Algebras},
  author = {Achim Blumensath},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 19, Issue 4},
  year = {2023},
  doi = {10.46298/lmcs-19(4:9)2023}
}