THERE IS NO FINITE-VARIABLE EQUATIONAL AXIOMATIZATION OF REPRESENTABLE RELATION ALGEBRAS OVER WEAKLY REPRESENTABLE RELATION ALGEBRAS
JEREMY F. ALM, Robin Hirsch, Roger D. Maddux · The Review of Symbolic Logic · 2016
Abstract We prove that any equational basis that defines representable relation algebras (RRA) over weakly representable relation algebras (wRRA) must contain infinitely many variables. The proof uses a construction of arbitrarily large finite weakly representable but not representable relation algebras whose “small” subalgebras are representable.