I am a retired physicist without experience in set theory. I found a variational formulation for causal sets that extracts invariat structures from symmetries (Complexity, Vol 17, pp. 19-38, 2011). In preliminary tests, these structures corresponded to physical observables.
I have reason to believe that there might be connections between my formulation and Turing invariants or Martin's conjecture, such as one being a particular case of the other.
I am seeking answers and/or a collaboration with a mathematician to search for possible connections. I can help discussing my formulation and I also have a computer setup that can do calculations if necessary.