Algebra Seminar talk
On a stronger reconstruction notion for transformation monoids and clones
We discuss the clone analogue of reconstruction of structures from their automorphism groups up to first order bi-definability. Rubin's weak ∀∃-interpretations play a key role. For clones over the monoids of self-embeddings of certain countable homogeneous relational structures including (ℚ,<), the random graph, the random digraph and the random tournament) we obtain positive results, for some others we present partial answers.