In this article we establish the undecidability of representability and of finite representability as algebras of binary relations in a wide range of signatures. In particular, representability and finite representability are undecidable for Boolean monoids and lattice ordered monoids, while representability is undecidable for Jónsson's relation algebra. We also establish a number of undecidability results for representability as algebras of injective functions.
"Undecidability of representability as binary relations." J. Symbolic Logic 77 (4) 1211 - 1244, December 2012. https://doi.org/10.2178/jsl.7704090